# Inverse Matrix Calculator

To find the inverse of matrix, choose the order of the matrix, input the entries of the matrix, and click calculate button using inverse matrix calculator

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## Matrix Inverse Calculator

Inverse matrix calculator solves a matrix to find its reverse using the elementary row and column elimination. It will give the whole process of finding the inverse of the matrix.

## What is the inverse of the matrix?

The reverse of the original matrix is called its inverse. It is often denoted by A-1. When a matrix is multiplied by its inverse, it gives the identity matrix. This trick can help to verify the accuracy of the inverse matrix.

## Matrix inverse formula:

The formula used for the inverse matrix is:

A-1 = (1/ |A|) . adj A

Where

This formula helps in a 2x2 square matrix better. For 3x3 or bigger matrices, mostly the elementary transformation is used.

## How to calculate the inverse of a matrix?

There are basically four methods, two of which are discussed above. The list of these methods is:

1. Inverse matrix calculator.
2. Using the formula.
3. Elementary transformations.
4. Finding the cofactors.

The calculator uses the second last method. There are two ways to carry out this transformation; row elimination and column elimination. The rows are subtracted or added and multiplied to each other and in some cases both.

1. Write the equation A=I.A, where I is the identity matrix of the same order.
2. The transformation will be applied on the A at the LHS and I on the RHS. the A on the RHS will remain intact.
3. Perform different techniques on the Left-hand side A to make it an identity matrix. Make the same changes to the identity matrix regardless.
4. When the A has become the identity matrix, the original identity matrix I would now be different and called matrix B. That is I=BA.
5. I=BA is equal to A-1=B, hence B is the inverse of matrix A

### Example: (row elimination)

Find the inverse of the following matrix:

Solution:

Step 1: Write the formula.

A=l.A

Step 2: Subtract the R1 multiplied by 3 from R3.

Step 3: Divide R2 by 2.

Step 4: Subtract R2 multiplied by 3 from R1.

Step 5: Multiply R2 by 8 and add it to R3.

Step 6: Divide R3 by 5.

Step 7: Multiply R3 by 2 and add it to R1.

Step 8: Subtract R3 from R2.

An identity matrix on LHS is obtained. Hence I = BA or A-1 = B.