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Determinants
Question
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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

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Answer

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P3= Q3
P3– P2Q = Q3– Q2P
P2(P – Q) = Q2(Q – P)
P2(P – Q) + Q2(P – Q) = O
(P2+ Q2)(P – Q) = O
⇒ |P2+ Q2| = 0

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