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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.

Table of Contents:

## 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 (R _{1}/5)*

*R _{2} => R_{2} - 15R_{1}*

*R _{3} => R_{3} - 10R_{1}*

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

*Divide row 2 by -25 (R _{2}/-25)*

*R _{1} => R_{1} - 2R_{2}*

*R _{3} => R_{3} - 5R_{2}*

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

*Divide row 3 by -20 (R _{3}/-20)*

*R _{1} => R_{1} - 1R_{3}*

*R _{2} => R_{2} - 1R_{3}*

The final** A^{-1} **can be written as,

**References: **

- Inverse of a Matrix by mathsisfun.com.
- Mathwords: Inverse of a Matrix.