Online Matrix Calculator [Addition, Subtraction, Multiplication, Division, Inverse]

Hello everyone, our today topic is matrix calculator. A matrix consists of certain number of rows and columns. You can also say a rectangular array defines a matrix. This matrix may have same number of row and columns and may these numbers can vary. It is quite difficult to solve these matrixes. So here, in this article I will share information about matrix calculator so, that you can easily solve these matrixes.

Matrix Calculator with Steps

There are various kinds of matrixes you need to solve like matrix multiplication, inverse matrix, augmented matrix, matrix determinant, Diagonalize matrix, Adjoint matrix, matrix transpose and so on. So, to solve all these numerous types matrix you need to know all the concepts regarding these and there is matrix calculator available for all types of matrixes. You can take help of corresponding calculator to solve the respective matrix. Here, in this article I will discuss about all the matrixes I have mentioned above. Matrix calculator helps us to solve these matrix problems very easily and within very short time span.

Matrix Algebra Calculator


Matrix is the important part of the Algebra mathematics. And if you are seeking to find out results of these matrix problems then you can choose matrix algebra calculator this calculator consists of all types of methods operations and functions you need to know about in matrix and want to solve questions of matrix of any type. Yup just need to choose the required function and then order of matrix and elements of the matrix and the required resultant will be appeared on the screen along with explanation option. If you want to have a look at the explanation then you can have a look at the explanation as well.


Matrix Multiplication Calculator


You are going to perform multiplication in matrix. Multiplication for 1 x 1 or 2 x 2 matrix can be very easily solved. But the complexity of these multiplication increases when the no. of rows and columns increases in the matrix.  Multiplication can only be performed if both the matrixes are of same sizes. That is if one matrix is 3×2 type then it can only be multiplied by the 3×2 type of other matrix. If both matrixes are not same then multiplication is not possible. To perform multiplication if need to perform dot product of rows and columns and the result matrix also come of same size as the matrixes are multiplied. In case of large sizes the complexity increases and to cross check your answer is correct or not you can use matrix multiplication calculator. This calculator is online available you can get this very easily.

Inverse Matrix calculator


Inverse of matrix can be computed with the help of identity matrix. Identity matrix has diagonal elements as 1 and rest elements are zero. You need to multiply your matrix A with the identity matrix I is will result to find out the inverse of matrix that is A-1. To find out inverse of matrix “A” you should know the multiplication concept of the matrix. You need to perform elementary transformations on the both sides of matrixes. I.e. A= IA. Until you reach the result I = BA. Here, the B stands for A-1. You need to apply right steps of transformations only then you will be able to find out correct answer. You can take help of inverse matrix calculator for this. Online there is each step description based on the required question of the inverse matrix you need to find out answer.


Augmented Matrix Calculator

 Augmented matrix is mostly used to solve the equations in which you have to find out the values of x, y, z. In case of augmented matrix you append rows and columns of the matrixes i.e. you have equation AX = B and you append A|B and then covert A into identity matrix to find out the value of X. In case of calculator you need to write down the values of A and B to find out the result showing values of X. You can have this calculator at internet services also.

Matrix Determinant Calculator


Determinant can be obtained of Square matrixes. As we all know the matrix consists of elements and to find out the determinant of the matrix you need to cross multiply each element with the diagonal element and after that subtract the product of the element with the other product of the element.

Suppose you have matrix

Aij =      | a1 b1|

|a2 b2|

Now, to find out the determinant we will subtract product of a1b2 from product of a2b1. Similarly to find out the determinant of 3×3 matrix we need to perform expansion of 3 rows and 3 columns. Like firstly we expand the a11 in which we take (-1)sum of suffix of a11 and determine the second order determinant of diagonal elements a22 b23 a33 and b33. Similarly we expand other rows and columns. And in the end determinant of A i.e. |A| is find out by subtracting the result.


i.e. |A| = a11 (a22a33 – a32a23) – a12 (a21a33 – a31a23) + a13 (a21a32 – a31a22)

To after the 3×3 matrix the complexity of finding out determinant of higher order of matrixes becomes difficult to find out. To find out determinant of any kind order of matrix you can use matrix determinant calculator. These calculate helps to reduce the complexity of long calculations and accuracy of the result as well.

Matrix Reduction Calculator

In the reduction method of matrix you need to transform the matrix into identity matrix and the result comes is known as matrix reduction. To find out result of matrix reduction with the help of calculator you simply need to enter a number of rows and columns first and then you will asked to write down the values of elements of the row and columns respectively. Click on the submit button. You can choose row reduction method or column reduction method as per your choice. But most of the times redaction method is performed with the help of rows. You will get the required answer along with the description of each step of matrix reduction method.

Online Matrix Calculator

Online matrix calculator helps a lot to find out the correct answers of the sums. You just need to enter the order of matrix and elements of the particular rows and columns to find out the required answers of the matrix. As there are various kind of methods and types of matrices whose calculations are very much complicated to solve and there are very high rate of chances to perform any mistake while performing long calculations. These online calculators explains each step of the method very well that you can easily find out your mistake and get the required result within  the very less passage of time that is in seconds. There isa large number of online calculator sites available to find out results of matrix.

Diagonalize Matrix Calculator

Diagonalize matrix is the matrix in which you have diagonal elements only. And if you have any question in which you are asked to Diagonalize the matrix, this simply means that you have to make other elements of the matrix zero not diagonal element. It is not necessary to convert diagonal elements to 1. If diagonal elements are 1 then the matrix considered to be the identity matrix. In case of Diagonalize matrix the diagonal element can possess any values except zero.  So, to make any matrix Diagonalize matrix you can choose Diagonalize matrix calculator for this. In this case in calculator you only need to write down the values and you will get the result along with description of each step which is used to convert the matrix to Diagonalize matrix.

Matrix RREF Calculator

Here, RREF stands for reduced row echelon formula. In this method we have to reduce the matrix into identity matrix with the help of row reduction. You can very easily find out the calculator stating matrix RREF calculator online which depicts answer of matrix along with the explanation of each step of reduced row echelon formula.

Matrix Row Reduction Calculator

Matrix row reduction simply performs steps to reduce the matrix into identity matrix.  Matrix row reduction calculator explains each operation which is performed on the specific rows to make the matrix an identity matrix.  These calculators are also known as matrix RREF calculator both works the same.


Inverse of a 3×3 Matrix Calculator

Inverse of a 3 x 3 matrix can also be finding out by simply performing transformation method. Like if your 3 x 3 matrix can be written as “A” and to find the inverse of take A = IA.  You can perform elementary row transformation on the matrix and firstly you can find out the determinant and if the determinant comes out to be zero then the inverse of the matrix does not exist. In the calculator you just only need to write down the order of the matrix. And one more thing in case of finding out the inverse of the matrix, the matrix need to be of Square matrix only then the inverse of the matrix can be find out. In case of 3 x 3 matrix mentioned the order of matrix 3 and then write down the values of each element to find out the result.


Adjoint Matrix Calculator


Adjoint matrix in simple terms is transpose of cofactor matrix. To find out the Adjoint firstly you need to find out the cofactor of the matrix. Than convert the cofactor matrix to the transpose matrix. The result will be considered as Adjoint matrix.


The Adjoint matrix can be represented as:

Adj = (C)T


If you are looking for Adjoint matrix calculator then you can find out online. This calculator will help to explain you each step of finding cofactor as well as taking transpose of the matrix as per your question. You just need to enter the values whose Adjoint matrix you want to find out.


Matrix Equation Calculator


Sometimes you have matrix in the equation form. And you need to find out the values of x, y, and z factors by solving this equation. In this case you should choose matrix equation calculator.

Matrix equation can be written as:

A1x + B1y +C1z  = X

A2x + B2y +C2z  = Y

A3x + B3y +C3z  = Z


You have values of A1, B1, C1, A2, B2, C2, A3, B3, C3 and X, Y, Z. You need to find out the values of x, y, and z respectively by solving this equation. Or sometimes you need to find out the missing values of elements also. So, to solve such kind of questions you should opt matrix equation calculator.

Matrix Addition Calculator


If you want to perform the addition of matrix then you need to first confirm that both the matrix should of same type that is value of i and j should be same in case of both matrices. After that to perform addition you will add same raw and column of both matrices. That is a11 of one matrix should be added to b11 of other matrix and so on. The resultant matrix also has same order of matrix in the end.


Cij = Aij + Bij


To find out addition of matrix you can choose matrix addition calculator.  In this case you have to write down same order of matrices for both and after that write down elements of each matrix to find out the right result. You can find this calculator online.


3×3 Matrix Calculator


3 x 3 matrix consists of 9 elements in it. There are various kinds of methods you need to implement on three by three matrixes. Like transpose, Adjoint, determinant, addition, subtraction, multiplication, reduction method etc. You can use any of method by the option which is available on the side bar menu. In 3 x 3 matrix there are 3 number of rows and 3 number of columns. You can search online for 3 x 3 matrix and perform the required method you want to implement on the matrix.


Matrix Transpose Calculator


Transpose of a matrix simply converts the rows into columns and columns into rows. For example the given matrix is of 3 x 2 type of matrix then the transpose of this matrix will be of 2 x 3. Transpose simply swap the values of rows and columns. And this transposition occurs the diagonal elements remain same in both the cases. It is very easy to find out the transpose of the matrix. But still if you are not clear with the concept of transpose and want to take help of calculator then there is online matrix transpose calculator available. You can take help of this to find out transpose.

Representation of transpose of the matrix:

Am x n = AT n x m

Matrix Rank Calculator


As we all know that sub matrix of the given matrix can be either of same number of rows and columns r we need to delete some rows and columns from it. The determinant of an r- rowed square sub matrix of given matrix is the minor of the matrix and if the minor of r-rowed comes out to be zero that means every minor of  higher order will also come out to be zero. So, the number r is considered as rank of the non-zero matrix if there exists one minor of order r of the matrix which does not vanish and also every minor of r+1 order if any vanishes. Rank of the matrix is simply determined by the minor of the matrix. And if the determinant comes out to be non-zero that means the rank of the matrix is same as the order of the matrix.

The rank of matrix is represented as:

ρ( A) = r


If the determinant comes out to be zero then the rank of the matrix will be less than the order of the matrix. Sometimes a little bit wrong calculation led to the wrong answer. So, you can use matrix rank calculator which is available online to check your answer is correct or not along with description of the result.

Matrix Power Calculator


Power of the matrix describes the number of copies of the matrix. If the power of the matrix is zero this means the matrix is of identity matrix. This simply means product of matrix with the same matrix as the number of power is mentioned. And it sometimes complicates the sum. If the power of matrix is 2, that means you need to multiply the given matrix with itself. You can find the product of two matrices and after that it becomes complicated foe us to find out product. So, to find out the result of power matrix you can use matrix power calculator. This will help you to find out the result of power matrix easily and within few seconds.


Cofactor matrix calculator

Cofactor of an element aij is denoted by Aij and this cofactor i defined by the (-1)i + j  Mij , where M is the minor of the aij. Minor are find out by finding the determinant of the element aij by deleting ith row and jth column of the matrix. These cofactors are used to find out the determinant of the matrix. You can use cofactor matrix calculator to find out the cofactors as while solving these cofactors most of the times there occur mistake in calculations by writing wrong sign. So, cofactor matrix calculator helps to find out your mistake also as they show details of each steps also.

Exponential matrix Calculator should be square matrix and this matrix has various rules as well. It is defined as the sum of power series. If the exponential is one that means the matrix is of identity matrix. You can find out transpose, conjugate, inverse of exponential matrix as well. And to perform all this operations you can take help of matrix exponential calculator. This calculator is also available online like other matrix calculators. You can use this to find out solutions of exponential of matrices.

Transition matrix is used to change the context of the matrix. This is based on the Markov’s chains law. Transition matrix is also known as stochastic matrix. It is also applied on square matrix. This includes transitions based on Markov’s law. This simply shows the change of vector spaces of the matrix. To solve transition matrix there is online calculator option. You can have this to solve transition matrix sums online.


Matrix Product Calculator

Product of the matrix can simply be solved similarly as I explained the multiplication of the matrix. Product of matrixes need to have both the matrix of same order otherwise the online product calculator will display no answer and this includes multiplication of each row with the columns of other matrix. When to find out answers of product of matrix online with the help of calculator then you will have clear idea of these steps which are implemented to solve the product of matrix.

Matrix Eigen Value calculator

Eigenvalue is used to find out the vector. This Eigen value is represented as:

A.v = λ·v

Where, λ is a scalar and this Eigen value can be applied on real as well as on complex values. This Eigen value is also known as characteristic value. This Eigen value is also implemented on square matrix that is matrix should be of n x n order. And there is online calculator also available to solve these Eigen value matrix problems and you can easily get these calculators online.


Matrix Subtraction Calculator                                             

In case subtraction also you need to have both the matrix of same type and the resultant matrix is also of same type. This subtraction operation is implemented by simply subtracting respective row of one matrix with the same row of other matrix. This is quite easy to find out addition and subtraction of the matrix as compare to perform other operations on the matrix. There are online subtraction calculators also to solve these matrix subtraction problems.

ax=b Matrix Calculator

ax = b is the equation matrix. This kind of matrix is solved to find out the value of x. Bu applying elementary transitions on the “a” and “b”. These linear equations are also used to find out the consistency of the systems. To find consistency you just need to concentrate upon the determinant values. Determinants help to check whether the equation is consistent or inconsistent. Inconsistent system has no solution while on the other hand the consistent system has one or many solutions. There is Jordan method, Eigen Values option to solve this kind of matrix. You need to choose the required method to solve this ax = b matrix online with the help of calculator as well.


Inverse of 2×2 matrix calculator

It is quite easy to find out inverse of 2 x 2 matrix as compare to find out the inverse of 3 x 3 matrix. Inverse of the matrix can be solved by simplifying the matrix into identity matrix. That is A = IA. In which you convert the left side A matrix into identity matrix by applying elementary transition whether row wise or column wise. And after that the resulted matrix of I is considered as inverse of A. These can be solved very easily with the help of calculator of the Inverse matrix. You just need to wrote down values of 2 x 2 matrix in t and then you will get the result of inverse of matrix along with description of steps which are performed to find out the inverse. These calculators also help you to clarify the each step of the method.

There are linear equations in the matrix which are solved with the help of determinants to check the consistency of the system. There are two types in it:

  • Consistent system: if the equation has one or more than one solution.
  • Inconsistent system: if the equation has no solution

So, to find out whether the system is consistent or not we need to solve the equations of the matrix. There is online matrix equation calculator available which helps to check the consistency of the system of equations.

These matrix calculators which are available online come with steps. They describe each step which is implemented to solve the required matrix. Whether you have to find out rank, minor, cofactor, transpose, product, addition or subtraction or any other operation on the matrix, these online matrix calculators have description of all the applied operation on the sum. This is the big advantage of using these calculators as you get clarity of the solution as well.

Matrix division calculator

There is no direct term as the division in the matrix. You can perform addition, subtraction, multiplication on the matrix. But still if you are looking for division of matrix then you will be the solution of finding inverse. This simply includes the steps AB = AB-1. And you need to follow the steps of inverse method init. And you can also get online calculator to find out division of matrix as well which explains and follow same inverse steps in it. This division of the matrix also need to have both the matrix of same order only then the division or inverse of the matrix can be find out.

Dot product of the matrix means multiplication of one matrix with the other matrix.  This means that you need to multiply each value of rows to the columns of other matrix and then add the product for finding each value of the resultant matrix. There is the option of online matrix dot product also which includes the steps of multiplication of matrix. Dot products are usually applied in case of vector formations of the matrices. You can take help of this calculator as this calculator also expands the steps which are involved to solve the matrix dot products.

The projection Matrix  Calculator also needs to have same type of square matrices. This is represented as an arrow on the head of the elementary value. A projection is used to check the vector projection to the other subspace. You a provided with two square matrices in which you need to find out the projection of one matrix on the other. Online calculators helps to compute these projection matrix along with the description of projection as well.

Matrix reducer calculator is used for the reduction methods implementation on the matrix. You just need to write down the values of matrix and order and you will get results on the basis of row or column wise reduction method.

The rotation matrix is used to find out the rotation in the Euclidean space. With the help of Cartesian coordinate system values of xy plane id determined and with the help of angle Ø.  And checked whether the rotation is counter clock wise or anti clock wise. This rotation matrix calculator helps to evaluate all these concepts of Euclidean space.

Adjugate matrix is other name of the Adjoint matrix. Adjoint matrix sometimes pronounced as Adjugate matrix. When you search of Adjugate matrix calculator you will find out same steps which you have performed or implemented in case of Adjoint matrix. This also calculates transpose of the cofactors of the matrix.

The Adjugate matrix is also represented as:

Adj = (C)T 

Invertible matrix calculators are used to finding out the inverse of the matrix. In this case you only have to write down the matrix order and elements no need to perform elementary transaction on the matrix to find out the answer. All the steps will be displayed on the screen to evaluate the inverse of given matrix.

This is all about the concepts and online calculators options for each type of matrix solution you are looking for. Hope this article has helped you to guide you on the right track and you get clearance of all the concepts to some extent. As the matrix is a very vast topic and you need to give attention and good grasp on calculation as well to improve your skills in it. And off course there is option of online matrix calculator also to help you in it.