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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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Table of Contents:

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.

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,

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

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