By using elementary row operations, find the inverse of the matrix
`A=[{:(3,-1),(-4," "2):}].`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 3 & -1 \\ -4 & 2 \end{pmatrix} \) 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.

### Step-by-Step Solution:

1. **Set Up the Augmented Matrix**:
We start with the augmented matrix \( [A | I] \):
\[
\begin{pmatrix}
...