Question

If A = [(1, 2, 2), (2, 1, 2), (2, 2, 1)], show that A² - 4A - 5I = 0, where I and 0 are the unit matrix and the null matrix of order 3, respectively. Use this result to find A^-1.

Answer 1

Given

Therefore,

A² - 4A - 5I = 0 ⇒ 5I = A² - 4A

By multiplying by A^-1, we get

5A^-1 = A - 4I