If $A=\left[\begin{array}{ccc}1 & -1 & 1 \ 0 & 2 & -3 \ 2 & 1 & 0\end{array} ight]$ and $B=\operatorname{adj} A, C=5A$, then $\frac{|\operatorname{adj} B|}{|C|}=$

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If $A=\left[\begin{array}{ccc}1 & -1 & 1 \ 0 & 2 & -3 \ 2 & 1 & 0\end{array}ight]$ and $B=\operatorname{adj} A, C=5A$, then $\frac{|\operatorname{adj} B|}{|C|}=$

Aicharya · Accepted Answer

$\begin{aligned} & A=\left|\begin{array}{ccc}1 & -1 & 1 \ 0 & 2 & -3 \ 2 & 1 & 0\end{array}ight| \ & \Rightarrow|A|=1 	imes(0+3)+1 	imes(0+6)+1 	imes(0-4)=5 \ & \because B=\operatorname{adj} A \ & \Rightarrow|B|=|\operatorname{adj} A|=|A|^2=25 \ & \Rightarrow|\operatorname{adj} B|=|B|^2=625 \ & \because C=5 A \ & \Rightarrow|C|=|5 A|=5^3|A|=125 	imes 5=625 \ & 	ext { now } \frac{|\operatorname{adj} B|}{|C|}=\frac{625}{625}=1\end{aligned}$

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0\end{array}\right]$ and…

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