# Nonsingular Matrix

**Nonsingular Matrix:**

A square n n matrix A is said to be non singular or invertible if there is another n n matrix B such that;

In this case the matrix B is called the inverse of A and is commonly denoted by A^{-1} rather than B. Otherwise the matrix A is called singular or non invertible.

**Example:1
**

Since AB = BA = I2, we conculde that B is the inverse of A.

**Proof:
**

Because of these uniqueness, we write the inverse of a non singular matrix A as A^{-1}

**Exampel-2:** Consider

Equating corresponding entries of these two matrices;

Since the matrix is;

We conclude that A is non singular matrices;