If the value of a third order determinant is 12 , then the value of the determinant formed by replacing each element by its cofactor will be 144.

Correct Answer True

Let $A$ is the determinant.
$\therefore$ $|A| = 12$

Also, we know that, if $A$ is a square matrix of order $n$,

then $\mid$ ${\left. {\left| {adjA} \right| = |A} \right|^{n - 1}}$

For $n = 3,$ $|{\mathop{\rm adj}\nolimits} A| = |A{|^{3 - 1}} = |A{|^2}$

$= {(12)^2} = 144$