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,$|C| = 16^2 = 256$.

Element	Co-factor
$A$. $-1$	$(1)$ $-2$
$B$. $1$	$(2)$ $32$
$C$. $3$	$(3)$ $4$
$D$. $6$	$(4)$ $6$
	$(5)$ $-6$

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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Match the following elements of the matrix $A = \left[\begin{array}{ccc} 1 & -1 & 0 \\ 0 & 4 & 2 \\ 3 & -4 & 6 \end{array}\right]$ with their co-factors and choose the correct answer.
Element Co-factor
$A$. $-1$ $(1)$ $-2$
$B$. $1$ $(2)$ $32$
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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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