For a $3 imes 3$ matrix A, if $\mathrm{A}(\operatorname{adj} \mathrm{A})=\left[\begin{array}{ccc}-10 & 0 & 0 \ 0 & -10 & 2 \ 0 & 0 & -10\end{array} ight]$, then the value of determinant of $\mathrm{A}$ is

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For a $3 	imes 3$ matrix A, if $\mathrm{A}(\operatorname{adj} \mathrm{A})=\left[\begin{array}{ccc}-10 & 0 & 0 \ 0 & -10 & 2 \ 0 & 0 & -10\end{array}ight]$, then the value of determinant of $\mathrm{A}$ is

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { We have }|\mathrm{A}(\operatorname{adj} \mathrm{A})|=\left[\begin{array}{ccc}-10 & 0 & 0 \ 0 & -10 & 2 \ 0 & 0 & -10\end{array}ight] \ & 	herefore|\mathrm{A}||\operatorname{adj} \mathrm{A}|=(-10)(100)=-1000 \ & 	herefore|\mathrm{A}||\mathrm{A}|^{3-1}=-1000 \Rightarrow|\mathrm{A}|^3=-1000 \Rightarrow|\mathrm{A}|=-10\end{aligned}$

For a $3 \times 3$ matrix A, if $\mathrm{A}(\operatorname{adj} \mathrm{A})=\left[\begin{array}{ccc}-10 & 0 &…

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