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(D) Given that $A$ and $B$ are square matrices of order $n=3$. We are given $|A|=2$ and $|B|=4$. We need to find $|A(\operatorname{adj} B)|$. Using th

Vedclass · Accepted Answer

$32$

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(D) Given that $A$ and $B$ are square matrices of order $n=3$. We are given $|A|=2$ and $|B|=4$. We need to find $|A(\operatorname{adj} B)|$. Using the property of determinants,$|AB| = |A||B|$,we have: $|A(\operatorname{adj} B)| = |A| |\operatorname{adj} B|$. We know that for a square matrix $B$ of order $n$,$|\operatorname{adj} B| = |B|^{n-1}$. Here $n=3$,so $|\operatorname{adj} B| = |B|^{3-1} = |B|^2$. Substituting the values: $|A(\operatorname{adj} B)| = |A| 	imes |B|^2 = 2 	imes (4)^2$. $|A(\operatorname{adj} B)| = 2 	imes 16 = 32$.

If $A$ and $B$ are square matrices of order $3$ such that $|A|=2$ and $|B|=4$,then $|A(\operatorname{adj} B)| = \dots$

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