Question

If for a matrix A, A² + I = O where I is the identity matrix, then A equals

(A) [(1, 0), (0, 1)]

(B) [(i, 0), (0, i)]

(C) [(1, 2), (-1, 1)]

(D) [(-1, 0), (0, -1)]

Answer 1

Answer is (B) [(i, 0), (0, i)]

A² + I = 0 ⇒ A² = [(-1, 0), (0, -1)]  of (I is of second order) ⇒ ((i, 0), (0, i))