If A = find x and y such A2 – xA + yI = O. Hence, evaluate A – 1.
A =
A2 =
=
Now, A2 – xA + yI =
= 22 – 4x + y = 0 or 4x – y = 22
= 18 – 2x = 0 or X = 9
= Y = 14
So, A2 – 5A + 7I = 0
Multiply by A – 1 both sides
= A.A. A – 1 – 9A. A – 1 + 14I. A – 1 = 0
= A – 9I + 14 A – 1 = 0
= A – 1 =
= A – 1 =
= A – 1 =