By using elementary operations, find the inverse of the matrix `A=[[1, 2], [2, -1]]`.

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 1 & 2 \\ 2 & -1 \end{bmatrix} \) using elementary operations, we will follow these steps:

### Step 1: Set up the augmented matrix
We start by writing the matrix \( A \) alongside the identity matrix \( I \):
\[
\left[ \begin{array}{cc|cc}
1 & 2 & 1 & 0 \\
2 & -1 & 0 & 1
...