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
-
0
-
-1
Solution
C.
0
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
