For a $3 imes 3$ matrix $M$, let trace $(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3 imes 3$ matrix such that $|A|=\frac{1}{2}$ and trace $(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2 A))$, then the value of $|B|+$ trace (B) equals :

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For a $3 	imes 3$ matrix $M$, let trace $(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3 	imes 3$ matrix such that $|A|=\frac{1}{2}$ and trace $(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2 A))$, then the value of $|B|+$ trace (B) equals :

Aicharya · Accepted Answer

$\because \operatorname{tr}(A)=3 	ext { and }|A|=\frac{1}{2}$ Now, $B=\operatorname{adj}(\operatorname{adj}(2 A))=|2 A|^{3-2} \cdot(2 A)$ $=2^3|A| \cdot 2 A=8 A$ $\begin{aligned} & 	herefore \operatorname{tr}(B)=8 \operatorname{tr}(A)=24 \ & 	ext { and }|B|=|8 A|=8^3 \cdot \frac{1}{2}=256 \ & 	herefore \quad \operatorname{trace}(B)+|B|=24+256\end{aligned}$ $=280$ .

For a $3 \times 3$ matrix $M$, let trace $(M)$ denote the sum of all the diagonal elements of $M$. Let $A$…

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