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 \( I \) of the same size. The goal is to transform \( A \) into \( I \) while applying the same operations to \( I \) to obtain \( A^{-1} \).

### Step-by-Step Solution:

1. **Set up the augmented matrix**:
\[
\left[ \begin{array}{ccc|ccc}
0 & 1 & 2 & 1 & 0 & 0 \\
...