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Inverse Matrix Calculator

Select the number of equations in the matrix and enter the matrix values. Hit the Calculate button to calculate the inverse of a matrix using the calculator below.

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Matrix Inverse Calculator

Inverse matrix calculator is an online tool that finds the inverse of a matrix for given values of a matrix. It can calculate the inverse of 2x2, 3x3, 4x4, and 5x5 matrices.

Let’s find out how to calculate inverse of matrix without using matrix inverse calculator.

How to find the inverse of a matrix (3x3)?

System of equations in matrix can be solved using Crammer’s rule. To add, subtract or multiply matrices, matrix calculator could be a handy tool.

Inverse of matrix can be calculated using above calculator, but, here we will take the inverse manually.

Example:

Find the inverse of the following matrix A.

inverse matrix

Solution:

Step 1: Augment the matrix with identity matrix.

inverse matrix calculator

Step 2: Make zeros in column 1 except the entry at row 1, column 1 (pivot entry).

 

Divide row 1 by 5 (R1/5)

inverse matrix calculator

R2 => R2 - 15R1

Inverse matrix calculator

R3 => R3 - 10R1

Inverse matrix calc

Step 3: Make zeros in column 2 except the entry at row 2, column 2.

Divide row 2 by -25 (R2/-25)

inverse matrix

R1 => R1 - 2R2

inverse matrix calculator

R3 => R3 - 5R2

invere matrix calc

Step 4: Make zeros in column 3 except the entry at row 3, column 3 (pivot entry).

Divide row 3 by -20 (R3/-20)

inverse matrix calc

R1 => R1 - 1R3

inverse matrix calc

R2 => R2 - 1R3

inverse matrix

The final A-1 can be written as,

inverse matrix calc

In decimal form,

inverse matrix calculator

References: 

  1. Inverse of a Matrix by mathsisfun.com.
  2. Mathwords: Inverse of a Matrix.