Show that A = [(-8 5), (2 4)] satisfies the equation A^2 + 4A – 42I = O. Hence, find A^–1.

Question

Show that \(A=\begin{bmatrix}-8&5\\2&4\end{bmatrix}\)satisfies the equation A² + 4A – 42I = O. Hence, 

find A^–1.

Answer 1

\(A=\begin{bmatrix}-8&5\\2&4\end{bmatrix}\)

A² = \(\begin{bmatrix}-8&5\\2&4\end{bmatrix}\)\(\begin{bmatrix}-8&5\\2&4\end{bmatrix}\) =\(\begin{bmatrix}64+10&-40+20\\-16+8&10+16\end{bmatrix}\)

\(=\begin{bmatrix}74&-20\\-8&26\end{bmatrix}\)