Let P and Q be 3 3 matrices with P Q . If P^3=Q^3 and P^2 Q=Q^2 P , then determinant of (P^2+Q^2 ) is equal to

Step-by-step solution

P^3=Q^3P^3-P^2 Q=Q^3-Q^2 PP^2(P-Q)=Q^2(Q-P)P^2(P-Q)+Q^2(P-Q)=O (P^2+Q^2 )(P-Q)=O |P^2+Q^2 |=0