If possible using elementary row transformations, find the inverse of the following matrices.
(i) `[{:(2,-1,3),(-5,3,1),(-3,2,3):}]`

Explanation

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

### Step 1: Augment the matrix
We start by writing the augmented matrix \( [A | I] \):

\[
\begin{pmatrix}
2 & -1 & 3 & | & 1 & 0 & 0 \\
...