Mathematics

Problem

Show that the matrix

A = \begin{bmatrix} 5 & 6 \\ 4 & 3 \end{bmatrix}

satisfies the equation

A^2 - 8A - 9I = 0

, where

I

2 \times 2

identity matrix and

0

2 \times 2

zero matrix. Using this equation, find

A^{-1}