Using elementary transformations, find the inverse of the matrix`[[1, 3],[ 2, 7]]`

Explanation

To find the inverse of the matrix \(\begin{bmatrix} 1 & 3 \\ 2 & 7 \end{bmatrix}\) using elementary transformations, we will follow these steps:

### Step 1: Set up the augmented matrix
We start with the matrix \(A\) and augment it with the identity matrix. This gives us:
\[ \begin{bmatrix} 1 & 3 & | & 1 & 0 \\ 2 & 7 & | & 0 & 1 \end{bmatrix} \]

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