Using elementary transformations, find the inverse of the matrix`[[2,-3],[-1, 2]]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 2 & -3 \\ -1 & 2 \end{pmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to convert \( A \) into \( I \).

### Step-by-Step Solution:

1. **Set up the augmented matrix**:
\[
\left( \begin{array}{cc|cc}
2 & -3 & 1 & 0 \\
...