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

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To find the inverse of the matrix \( A = \begin{pmatrix} 2 & -3 \\ -1 & 2 \end{pmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to convert \( A \) into \( I \). ### Step-by-Step Solution: 1. **Set up the augmented matrix**: \[ \left( \begin{array}{cc|cc} 2 & -3 & 1 & 0 \\ ...
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