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

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 1 & -1 \\ 2 & 3 \end{pmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and then perform row operations to convert \( A \) into \( I \). The augmented matrix will look like this:

\[ \left( \begin{array}{cc|cc} 1 & -1 & 1 & 0 \\ 2 & 3 & 0 & 1 \end{array} \right) \]
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