If A is a square matrix 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 ${| A |}^{8}$
$∣ ∣ A d j (A d j A^{2}) ∣ ∣$
$Q = {∣ ∣ A^{2} ∣ ∣}^{(3 - 1)^{2}} = {∣ ∣ A^{2} ∣ ∣}^{4} = {| A |}^{8}$

${| A |}^{8}$

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∣ ∣ \begin{matrix} A d j (A d j A^{2}) \end{matrix} ∣ ∣ =

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∣ ∣ A d j (A d j A^{2}) ∣ ∣ =

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| A | = 2

∣ ∣ (a d j A^{- 1})^{- 1} ∣ ∣

If A is a square matrix of order 4 and the value of |A| is equal to 2. Then the value of |Adj(A)| is,

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