Obtain the inverse of the following matrix using elementary operations `A=[[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 operations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations until the left side becomes the identity matrix.

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

\[
\begin{bmatrix}
0 & 1 & 2 & | & 1 & 0 & 0 \\
...