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 to transform \( A \) into \( I \). The steps are as follows:

### Step 1: Set up the augmented matrix
We write the augmented matrix \( [A | I] \):
\[
\begin{pmatrix}
1 & 2 & 5 & | & 1 & 0 & 0 \\
2 & 3 & 1 & | & 0 & 1 & 0 \\
...