Inverse Matrix Calculator

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.

Solution:

Step 1: Augment the matrix with identity matrix.

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

Divide row 1 by 5 (R₁/5)

R₂ => R₂ - 15R₁

R₃ => R₃ - 10R₁

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

Divide row 2 by -25 (R₂/-25)

R₁ => R₁ - 2R₂

R₃ => R₃ - 5R₂

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

Divide row 3 by -20 (R₃/-20)

R₁ => R₁ - 1R₃

R₂ => R₂ - 1R₃

The final A^-1 can be written as,

In decimal form,