If A = [(1, 2, 2), (2, 1, 2), (1, 2, 1)], find A^–1 and prove that A^2 – 4A–5I = O.

Question

If \(A=\begin{bmatrix}1&2&2\\2&1&2\\1&2&1\end{bmatrix}\), find A^–1 and prove that A² – 4A–5I = O.

Answer 1

Also, A² – 4A – 5I = 0

Now, 6(A.A) A^–1 – 4.A A^–1 – 5I.A^–1 = 0

= A – 4I – 5A^–1 = 0