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  4. If the value of a third order determinant is 11, then the value of the square of the determinant formed by the cofactors will be

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Q. If the value of a third order determinant is $11$, then the value of the square of the determinant formed by the cofactors will be

Determinants

Solution:

$\Delta^{\prime}=\Delta^{n-1}$
$\therefore \Delta^{\prime}=\Delta^{3-1}=\Delta^{2}(\because n=3)$
$\Rightarrow \Delta^{\prime}=\Delta^{2}$
$\therefore \Delta^{\prime}=(11)^{2}$
$\Rightarrow \left(\Delta'\right)^{2}=\left(11^{2}\right)^{2}$
$=(11)^{4}=14641$