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Let A be a matrix of order $3 \times 3$ and det A= 3. Then $|(\det A) a d j (6 a d j (A^{2}))|$ is equal to

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$3^{17} \times 2^{17}$

$3^{14} \times 2^{17}$

$3^{14} \times 2^{14}$

$3^{17} \times 2^{6}$

answer is B.

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Detailed Solution

$|3 a d j (6 a d j (A^{2}))| = 3^{3} {|6 a d j (A^{2})|}^{2} = 3^{3} {(6^{3} |a d j (A^{2})|)}^{2}$

$= 3^{3} {.6}^{6} {|a d j A^{2}|}^{2} = 3^{3} {.6}^{6} {(|A^{2}|)}^{2} = 3^{3} {.6}^{6} {.3}^{8} = 3^{17} \times 2^{6}$

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