Question
If A2 – A + I = 0, then the inverse of A is
-
A + I
-
A
-
A – I
-
I – A
Solution
D.
I – A
Given A2 – A + I = 0
A–1A2 – A–1A + A–1 – I = A–1⋅0 (Multiplying A–1 on both sides)
⇒ A - I + A-1 = 0 or A–1 = I – A.
