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Adjoint of a Matrix

If adj B = A,...

Question

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

A

P Q

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B

Q A P

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C

P A Q

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D

P A^{- 1} Q

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Solution

The correct option is C $P A Q$
$adj (Q^{- 1} B P^{- 1}) = adj (P^{- 1}) adj (B) adj (Q^{- 1})$
$= \frac{P}{| P |} A \frac{Q}{| Q |}$
$= P A Q$

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