Using elementary transformations, find the inverse of the matrix`[[2 ,3], [5, 7]]`

Explanation

To find the inverse of the matrix \[ A = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \] using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to convert \( A \) into \( I \). The steps are as follows:

### Step 1: Set up the augmented matrix
We start with the augmented matrix \[ (A | I) \]:
\[
\begin{pmatrix}
2 & 3 & | & 1 & 0 \\
5 & 7 & | & 0 & 1
...