**Inverse of a Matrix**: Suppose **A** is an *n* x *n* matrix. The inverse of **A** is another *n* x *n* matrix which is denoted as **A ^{-1}** and satisfies the following conditions.

**AA ^{-1}** =

**A**=

^{-1}A**I**

_{n}Below, with an example, we illustrate the relationship between a matrix and its inverse.

**Does every Matrix have an inverse**?

There are two ways to determine of square matrix has an inverse:

- For any given matrix with dimensions equal to n*n, if Rank of Matrix is not less than n then matrix has inverse. In other words, Rank of the square matrix must be equal to its dimension
- Non-Zero Determinant. If determinant of a square matrix is non zero then inverse of a matrix exits

**How to Calculate Inverse of a Matrix**: Let us suppose we have a matrix a given below.

**Just do as mentioned**: **swap** the positions of a and d, put **negatives** in front of b and c and divide everything by the determinant i.e. (ad-bc).

A square matrix that has an inverse is said to be **non-singular** or **invertible**; a square matrix that does not have an inverse is said to be **singular**.