Find inverse, by elementary row operations (if possible) , of both following matrices. (i) ` [{:(1,3),(-5,7):}]` (ii) `[{:(1,3),(-2,6):}]`

Explanation

To find the inverse of the given matrices using elementary row operations, we will follow a systematic approach. Let's solve each matrix one by one.

### Part (i): Matrix A = \(\begin{pmatrix} 1 & 3 \\ -5 & 7 \end{pmatrix}\)

1. **Set up the augmented matrix**: We will augment the matrix \(A\) with the identity matrix \(I\):
\[ \begin{pmatrix} 1 & 3 & | & 1 & 0 \\ -5 & 7 & | & 0 & 1 \end{pmatrix} \]
...