Question

Show that A = \(\begin{bmatrix} -8 & 5\\[0.3em] 2 & 4 \end{bmatrix}\)satisfies the equation A² + 4A - 42I = 0.Hence find A^-1.

Answer 1

Given as

We have to prove A² + 4A - 42I = 0

= A^-1A.A + 4A^-1.A - 42A^-1I = 0