If $A$ ' is non-singular square matrix of order 3 then $| a d j (A^{3}) |$ equals

| A |^{8}

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| A |^{6}

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| A |^{9}

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| A |^{12}

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Solution

The correct option is B $| A |^{6}$
$A d j (A^{3}) = | A^{3} | (A^{3})^{- 1}$
$| A^{3} | = | A |^{9}$ , $| (A^{3})^{- 1} | = \frac{1}{| A |^{3}}$
$| A d j (A^{3}) | = | | A^{3} | (A^{3})^{- 1} |$
$| A d j (A^{3}) | = | | A^{3} | | | (A^{3})^{- 1} |$
$| A d j (A^{3}) | = | A |^{9} \frac{1}{| A |^{3}}$
$| A d j (A^{3}) | = | A |^{6}$

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If A' is non-singular square matrix of order 3 then |adj(A3)| equals

The correct option is B |A|6Adj(A3)=|A3|(A3)−1|A3|=|A|9, |(A3)−1|=1|A|3|Adj(A3)|=||A3|(A3)−1||Adj(A3)|=||A3|||(A3)−1||Adj(A3)|=|A|91|A|3|Adj(A3)|=|A|6

If $A$ ' is non-singular square matrix of order 3 then $| a d j (A^{3}) |$ equals