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Singular and Non Singualar Matrices

If adj B=A ...

Question

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

A

A P Q

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B

P A Q

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C

B

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D

A

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Solution

The correct option is A $A P Q$
$a d j ∣ ∣ A^{- 1} ∣ ∣ = \frac{A}{| A |}$

$a d j ∣ ∣ Q^{- 1} {B P}^{- 1} ∣ ∣ = a d j ∣ ∣ P^{- 1} ∣ ∣ * a d j | B | * a d j ∣ ∣ Q^{- 1} ∣ ∣ = \frac{P}{| P |} * A * \frac{Q}{| Q |} = P A Q$

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