If the value of a third order determinant is | vedclass

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(D) Let $A$ be a square matrix of order $n = 3$ such that $|A| = 16$. The matrix formed by replacing each element of $A$ with its cofactor is known as

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$256$

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(D) Let $A$ be a square matrix of order $n = 3$ such that $|A| = 16$. The matrix formed by replacing each element of $A$ with its cofactor is known as the cofactor matrix,denoted by $C$. The adjoint matrix $\operatorname{adj} A$ is the transpose of the cofactor matrix,i.e.,$\operatorname{adj} A = C^T$. We know that $|\operatorname{adj} A| = |A|^{n-1}$. Since the determinant of a matrix is equal to the determinant of its transpose,$|C| = |C^T| = |\operatorname{adj} A|$. Substituting the given values,we get $|C| = |A|^{3-1} = |A|^2$. Therefore,$|C| = 16^2 = 256$.

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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