Using elementary transformations, find the inverse of each of the matrices`[[2,-6],[ 1,-2]]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 2 & -6 \\ 1 & -2 \end{pmatrix} \) using elementary transformations, 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:

\[ \begin{pmatrix} 2 & -6 & | & 1 & 0 \\ 1 & -2 & | & 0 & 1 \end{pmatrix} \]

### Step 1: Make the leading coefficient of the first row equal to 1
We can achieve this by dividing the first row by 2:
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