Question

If A is a square matrix such that A³ = I then A^-1 is equal to

(A) I

(B) A

(C) A²

(D) None of these

Answer 1

Answer is (C) A²

A is a square matrix and A³ = I ⇒ A³ = I ⇒ A² × A = I.

So A² is the inverse of A

Hence, A^-1 = A².