Find the inverse using elementary row transformations: `[0 1 2 1 2 3 3 1 1]`

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \) using elementary row transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to convert \( A \) into \( I \). The augmented matrix will look like this:

\[
\left[ \begin{array}{ccc|ccc}
0 & 1 & 2 & 1 & 0 & 0 \\
1 & 2 & 3 & 0 & 1 & 0 \\
3 & 1 & 1 & 0 & 0 & 1
\end{array} \right]
...