Using elementary transformations, find the inverse of the matrix`[[6,-3],[-2, 1]]`

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 6 & -3 \\ -2 & 1 \end{bmatrix} \) using elementary transformations, we first need to check the determinant of the matrix.

### Step 1: Calculate the Determinant of Matrix A
The determinant of a 2x2 matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) is calculated using the formula:
\[ \text{det}(A) = ad - bc \]
For our matrix \( A \):
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