find the invese of the matraix `[(1,2,5),(2,3,1),(-1,1,1)],` using elementary row operaations.

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 1 & 2 & 5 \\ 2 & 3 & 1 \\ -1 & 1 & 1 \end{pmatrix} \) using elementary row operations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations until the left side becomes the identity matrix. The right side will then be the inverse of \( A \).

### Step-by-Step Solution:

1. **Set up the augmented matrix**:
\[
\left( \begin{array}{ccc|ccc}
1 & 2 & 5 & 1 & 0 & 0 \\
...