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If A is a $3 \times 3$ matrix and B is its Adjoint matrix. If the determinant of B is 36 then the determinant of A is

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$\pm 6$

$\pm 8$

$\pm 4$

$\pm 16$

answer is C.

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Detailed Solution

Given B=AdjA, n=3

And $| B | = |Adj A| = 36$

$|Adj A| = {|A|}^{n - 1} = {|A|}^{2} = 36$

$∴ |A| = \pm 6$

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