If `A=[{:(1,-1),(2,3):}]`, shown that `A^(2)-4A+5I=o`. Hence Find `A^(-1)`.

Explanation

To solve the problem, we need to show that \( A^2 - 4A + 5I = 0 \) and then find the inverse of matrix \( A \).

Given:
\[ A = \begin{pmatrix} 1 & -1 \\ 2 & 3 \end{pmatrix} \]

### Step 1: Calculate \( A^2 \)

To find \( A^2 \), we multiply matrix \( A \) by itself:
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