Let P and Q be 3 × 3 matrices with P ≠ Q

• Matrices Determinants

Let P and Q be 3 × 3 matrices with P ≠ Q. If P³ = Q³ and P²Q = Q²P, then determinant of (P² + Q²) is equal to

1. 0
2. 1
3. -1
4. -2

Answer

P³ = Q³

P³ - P²Q = Q³ - Q²P

P²(P - Q) = Q²(Q - P)

P²(P - Q) + Q²(P - Q) = 0

(P² + Q²)(P - Q) = 0

The correct option is A.