Using elementary transformations, find the inverse of the matrices`[[2, 5],[ 1, 3]]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations until we transform \( A \) 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 & 5 & | & 1 & 0 \\
1 & 3 & | & 0 & 1
...