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The value of a third order determinant is 11 then the value of the square of the determinant formed by the cofactors is

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121

${(121)}^{4}$

${(121)}^{3}$

${(121)}^{2}$

answer is B.

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Detailed Solution

Let $A_{3 \times 3}$

$\begin{array}{rcl} | A | & = & 11 \\ | Cofactor of A |^{2} & = & | ad j A^{T} |^{2} \\ = & | ad j A |^{2} \\ = & {[{(11)}^{2}]}^{2} \\ = & {(121)}^{2} \end{array}$

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