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
Answer & explanation
Correct answer: option 3
$|Q^{-1}P^2 Q|=4$
$⇒|Q^{-1}||P^2||Q|=4$
$⇒|P^2|=\frac{|Q|}{|Q|}=4$
$⇒|P|=±2$
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
Correct answer: option 3
$|Q^{-1}P^2 Q|=4$
$⇒|Q^{-1}||P^2||Q|=4$
$⇒|P^2|=\frac{|Q|}{|Q|}=4$
$⇒|P|=±2$