If $Q$ is non-singular matrix and \(P\

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If $Q$ is non-singular matrix and $P$ is a square matrix such that $\det(Q^{-1}P^2 Q)=4$ then $\det P$ is equal to

Options:

$0$

$1$

$±2$

$4$

Correct Answer:

$±2$

Explanation:

$|Q^{-1}P^2 Q|=4$

$⇒|Q^{-1}||P^2||Q|=4$

$⇒|P^2|=\frac{|Q|}{|Q|}=4$

$⇒|P|=±2$