If A[(4 5), (2 1)], then show that A – 3I = 2 (I + 3A^–1).

Question

If \(A=\begin{bmatrix}4&5\\2&1\end{bmatrix}\), then show that A – 3I = 2 (I + 3A ^–1).

Answer 1

\(A=\begin{bmatrix}4&5\\2&1\end{bmatrix}\)

|A| = 4 – 10 = – 6 adj \(A=\begin{bmatrix}1&-5\\-2&4\end{bmatrix}\)

Hence, A – 3I = 2 (I + 3A ^–1)