For a $3 imes3$ matrix $M$, let trace$(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3 imes3$ matrix such that $|A|=\frac12$ and trace$(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2A))$, then the value of $|B|+$ trace$(B)$ equals :

Question

For a $3	imes3$ matrix $M$, let trace$(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3	imes3$ matrix such that $|A|=\frac12$ and trace$(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2A))$, then the value of $|B|+$ trace$(B)$ equals :

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] For a $3	imes3$ matrix, $\operatorname{adj}(\operatorname{adj}M)=|M|\,M$. Here $|2A|=8\cdot\frac12=4$, so $B=4\cdot2A=8A$. Then $|B|=8^3\cdot\frac12=256$ and trace$(B)=8\cdot3=24$. Sum $=280$. Answer (4).

Q. For a $3\times3$ matrix $M$, let trace$(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3\times3$ matrix such that $|A|=\frac12$ and trace$(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2A))$, then the value of $|B|+$ trace$(B)$ equals :

Explanation

Reviewed by Dr. Abubacker

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