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

P3 = Q3, P2Q = Q2P on substraction, wegetP3-P2Q=Q-Q2PP2(P-Q)+Q2(P-Q)=0P2+Q2 P-Q=0but P≠Q,∴ P2+Q2=0∴ |P2+Q2|=0

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

P3 = Q3, P2Q = Q2P on substraction, wegetP3-P2Q=Q-Q2PP2(P-Q)+Q2(P-Q)=0P2+Q2 P-Q=0but P≠Q,∴ P2+Q2=0∴ |P2+Q2|=0

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Let P amd Q be 3 x 3 matrices with $P \neq Q$ . If $P^{3} = Q^{3}$ and $P^{2} Q = Q^{2} P$ , then determinant of $(P^{2} + Q^{2})$ is equal to

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Detailed Solution

$P^{3} = Q^{3}, P^{2} Q = Q^{2} P$

on substraction, weget

$\begin{array}{rcl} P^{3} - P^{2} Q & = & Q - Q^{2} P \\ P^{2} (P - Q) + Q^{2} (P - Q) & = & 0 \\ (P^{2} + Q^{2}) (P - Q) & = & 0 \\ but P & \neq & Q, \\ ∴ P^{2} + Q^{2} & = & 0 \\ ∴ | P^{2} + Q^{2} | & = & 0 \end{array}$

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

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Let P amd Q be 3 x 3 matrices with $P \neq Q$ . If $P^{3} = Q^{3}$ and $P^{2} Q = Q^{2} P$ , then determinant of $(P^{2} + Q^{2})$ is equal to