For an invertible matrix $A$, if $A(\operatorname{adj} A)=\left[\begin{array}{cc}20 & 0 \ 0 & 20\end{array} ight]$, then $|A|=$

Question

For an invertible matrix $A$, if $A(\operatorname{adj} A)=\left[\begin{array}{cc}20 & 0 \ 0 & 20\end{array}ight]$, then $|A|=$

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { We have } \mathrm{A}(\operatorname{adj} \mathrm{A})=\left[\begin{array}{cc}20 & 0 \ 0 & 20\end{array}ight] \ & 	herefore|\mathrm{A}||\operatorname{adj} \mathrm{A}|=\left[\begin{array}{cc}20 & 0 \ 0 & 20\end{array}ight] \Rightarrow|\mathrm{A}|\left(|\mathrm{A}|^{2-1}ight)=400 \Rightarrow(|\mathrm{A}|)^2=(20)^2 \ & \Rightarrow|\mathrm{A}|=20\end{aligned}$

For an invertible matrix $A$, if $A(\operatorname{adj} A)=\left[\begin{array}{cc}20 & 0 \\ 0 &…

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