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

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 2 & -1 \end{pmatrix} \) using elementary operations, we will augment the matrix \( A \) with the identity matrix and perform row operations to convert \( A \) into the identity matrix. The augmented matrix will look like this:

\[ \begin{pmatrix} 1 & 2 & | & 1 & 0 \\ 2 & -1 & | & 0 & 1 \end{pmatrix} \]

### Step 1: Eliminate the first column below the leading 1
We want to make the element in the second row, first column (2) equal to 0. We can do this by replacing Row 2 with Row 2 minus 2 times Row 1.
...