Using elementary transformations, find the inverse of the matrix`[[3,-1],[-4, 2]]`

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to convert \( A \) into \( I \).

### Step 1: Set up the augmented matrix

We start by writing the augmented matrix \( [A | I] \):

\[
\begin{bmatrix}
...