Using elementary transformations, find the inverse of the matrix`[[1, 3,-2],[-3, 0,-5],[ 2, 5, 0]]`

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations until the left side becomes the identity matrix. The right side will then be the inverse of \( A \).

### Step-by-Step Solution:

1. **Set Up the Augmented Matrix**:
\[
\left[ \begin{array}{ccc|ccc}
1 & 3 & -2 & 1 & 0 & 0 \\
...