Find the inverse of the matrix `A = {:((1,2,-2),(-1,3,0),(0,-2,1)):}` by using elementary row transformations.

Explanation

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

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

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