# Inverse of a Matrix

Recall that a simple linear equation of the form ** ax = b** has the solution

**,**

*x*=*b/a*= a^{-1}.b

*a ≠*0.As noted in earlier modules, a system of linear equations can be written as ** AX = B**, where

**and**

*A***are known matrices and**

*B***is the variable matrix. Note that this equation resembles a simple linear equation. The question is does the solution look like**

*X***? If so, what is**

*X*=*A*^{-1}. B**and how to find it?**

*A*^{-1}In this module we will learn about matrix inverse and use the same, if it exists, to find the solution to a system of linear equations.

**Review: **Augmented matrices and Gauss-Jordan Elimination method.

**Learning Objectives: **

- Square matrix, singular and non-singular matrices
- Identify matrix
- Inverse of a non-singular matrix
- Use the inverse, when it exists, to find the solution to a system of linear equations.