If $A$ is a square of order $3$ , then $∣ ∣ A d j (A d j A^{2}) ∣ ∣ =$

{| A |}^{2}

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{| A |}^{4}

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{| A |}^{8}

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{| A |}^{16}

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Solution

The correct option is C ${| A |}^{8}$
KEY: 3
$∣ ∣ a d j (a d j A^{2}) ∣ ∣$
$Q = {∣ ∣ A^{2} ∣ ∣}^{{(3 - 1)}^{2}} = {∣ ∣ A^{2} ∣ ∣}^{4} = {| A |}^{8}$

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∣ ∣ (a d j A^{- 1})^{- 1} ∣ ∣

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