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  4. If A is a square matrix of order 3 and | A | = 8, then | adj A |=

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Q. If $A$ is a square matrix of order $3$ and $| A | = 8$, then $| adj\, A |=$

COMEDKCOMEDK 2007Determinants

Solution:

$| A | = 8,$ order of $A$ is 3.
We know that $| adj\: A | = | A |^{n-1}$
Here, $n = 3$ and $| A | = 8$
$\therefore \, \, |adj \: A| =8^{3-1} =8^2$.