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

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{pmatrix} \) using elementary column transformations, we will augment the matrix \( A \) with the identity matrix of the same order. The steps are as follows:

### Step 1: Set up the augmented matrix
We augment the matrix \( A \) with the identity matrix \( I \):
\[
\left( \begin{array}{ccc|ccc}
1 & 0 & 1 & 1 & 0 & 0 \\
0 & 2 & 3 & 0 & 1 & 0 \\
...