If `A=[(2,-3),(3,4)],` show the `A^2-6A+17I=0.` Hence find `A^-1`

Explanation

To solve the problem, we need to show that \( A^2 - 6A + 17I = 0 \) and then find \( A^{-1} \). Let's go through the solution step by step.

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

Given the matrix \( A = \begin{pmatrix} 2 & -3 \\ 3 & 4 \end{pmatrix} \), we first calculate \( A^2 \):

\[
A^2 = A \cdot A = \begin{pmatrix} 2 & -3 \\ 3 & 4 \end{pmatrix} \cdot \begin{pmatrix} 2 & -3 \\ 3 & 4 \end{pmatrix}
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