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Combination

If B=A, |...

Question

If $B = A$ , $| P | = | Q | = 1$ , then $a d j (Q^{- 1} {B P}^{- 1)}$ is

A

P . Q

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B

Q . a d j (A) . P

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C

P . a d j (A) . Q

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D

P . A^{- 1} . Q

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Solution

The correct option is C $P . a d j (A) . Q$
Given, $B = A, | P | = | Q | = 1$
Consider, $a d j (Q^{- 1} {B P}^{- 1)}$
$= (a d j P^{- 1}) (a d j B) (a d j Q^{- 1}) (∵ a d j (A B C) = (a d j C) (a d j B) (a d j A)$
$= \frac{P}{| P |} (a d j B) \frac{Q}{| Q |} (∵ a d j P^{- 1} = \frac{P}{| P |})$
$= P (a d j A) Q$ ( $∵ A = B$ )

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