Question

If A = (\begin{bmatrix} 2& 3 \[0.3em] 1&2 \end{bmatrix})verify that A2 - 4A + I = 0, where I = (\begin{bmatrix} 1& 0 \[0.3em] 0&1 \end{bmatrix})and O =(\begin{bmatrix} 0& 0\[0.3em] 0&0\end{bmatrix}). Hence find A-1.

Answer 1

Considering the

A2 - 4A + I = 0

A.A - 4A = - I

On multiplying by A-1 both side