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  4. If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

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Q. If the value of a third order determinant is $16$, then the value of the determinant formed by replacing each of its elements by its cofactor is

KCETKCET 2019Determinants

Solution:

$\left|A\right|=16, O\left(A\right)=3$
$\left|adj \, A\right|=\left|A\right|^{2}$
$=16^{2}$
$=256$