Given A = [(2 -3), (-4 7)], compute A^–1 and show that 2A^–1 = 9I – A.

Question

Given \(A=\begin{bmatrix}2&-3\\-4&7\end{bmatrix}\), compute A^–1 and show that 2A^–1 = 9I – A.

Answer 1

\(A=\begin{bmatrix}2&-3\\-4&7\end{bmatrix}\)

|A| = 14 – 12 = 2 adj \(A=\begin{bmatrix}7&3\\4&2\end{bmatrix}\)

Hence, 2A ^–1 = 9I – A