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 :

Engineering

Mathematics

Inverse of a Matrix

Question

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 :

–2

–1

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P³ = Q³

P²Q = Q²P

P³ – P²Q = Q³ – Q²P

P² (P – Q) = Q² (Q – P)

(P² + Q²) (P – Q) = 0

| P² + Q² | | P – Q | = 0

| P² + Q² | = 0 or | P – Q | = 0.