# Matrix A

Column
Row

## Introduction to the Matrix Multiplication Calculator

A matrix multiply calculator is an online tool that can multiply two matrices of the same order. It applies the multiplication formula on two matrices whose order can be up to 4. It is calculated step-by-step to avoid the complexity of the matrix multiplication method.

In matrix algebra, the multiplication of matrices is an essential concept that you always need to solve 3x3 matrix multiply. Finding the multiplication of matrices by a tool online is brighter than solving it manually. We are introducing a tool online that can calculate expansion easily.

## The formula used by Multiplication of Matrix Calculator

Matrix multiplication is one of the operations performed in matrix algebra. But the matrix multiplication is not simple as the addition and subtraction of the matrices. The multiplication calculator follows the rule of multiplication of matrix, which is:

“Two matrices can be multiplied only when they are compatible. It means that for the multiplication of matrices, the number of columns in the first matrix should equal the number of rows in the second matrix.”

Let’s see how the multiplication of two matrices performed of order 2×2

$$A \;=\; \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \; AND \; \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix}$$

## How to Multiply Matrices

There are some steps to multiply two matrices by using matrix multiplication formula:

1. Please select the first row of matrix A and the first column of matrix B. Multiply each corresponding entry of the selected row and column and then add them. It will give the first element of the resultant matrix.
2. Now select the second row of matrix A and the first column of matrix B, multiply each corresponding entry of the selected row and column, and then add them. It will give the 2nd entry of the column of the resultant matrix.
3. Similarly, repeat the procedure by selecting rows of the matrix A and the second column of matrix B.
4. The resultant matrix will be:

$$C \;=\; A \times B \;=\; \begin{bmatrix} a_{11}.b_{11}+a_{12}.b_{12} & a_{11}.b_{12}+a_{12}.b_{22} \\ a_{21}.b_{11}+a_{22}.b_{21} & a_{21}.b_{12}+a_{22}.b_{22} \end{bmatrix}$$

Or it can be written as:

$$C \;=\; \begin{bmatrix} c_{11} & c_{12} \\ c_{21} & c_{22} \end{bmatrix}$$

## How to use the Matrix Multiplication Calculator with steps?

There are some simple steps to using this tool. These steps are:

1. Enter the number of rows and columns for matrix A and then enter the values of all its entries.
2. Now again, select the number of rows and columns for matrix B and then write the values of all B entries.
3. You can use the random button to select random values of A and B instead of writing manually.
4. Now click on the calculate button.
5. You will get the result a few seconds after clicking on the calculate button.

## Why use the Matrix Multiply Calculator?

In mathematics, the multiplication of matrices is an important concept. But this procedure is somehow tricky and lengthy. Many students face many difficulties in solving the multiplication of matrices. They ignore the multiplication rules. So they always need external help that makes this method easy for them. That’s why the students can use this matrix multiplication tool to evaluate multiplication with a step-by-step solution.

## Benefits of using Matrix Multiplication Formula Calculator

This tool has many beneficial uses to improve your problem-solving skills in mathematics. These benefits are:

1. It is an online free tool so that you don’t need to pay any fee for 2x2 matrix multiply.
2. Multiplication of matrix calculator is helpful for students that it solves the problem step-by-step in which every single multiplication is involved.
3. Matrix multiply calculator saves your time from doing manual computations.
4. It can handle up to the 4th order of matrices.
5. Matrix multiplication calculator can be beneficial for you to solve many real-life problems.
6. It has a random option that allows you to practice with many issues about how to multiply matrices. ### Hamza Haroon

Last Updated April 05, 2022

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