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If $\mathrm{A}(\operatorname{adj} \mathrm{A})=5 \mathrm{I}$ where $I$ is the identity matrix of order 3 , then $\mid$ adj $A \mid$ is equal to
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The correct answer is:
25
Given, $A(\operatorname{adj} A)=5 I$
$$
\begin{aligned}
&\therefore \quad|\mathrm{A}| \mathrm{I}=5 \mathrm{I} \Rightarrow|\mathrm{A}|=5 \\
&\therefore \quad|\operatorname{adj}(\mathrm{A})|=|\mathrm{A}|^{3-1}=|\mathrm{A}|^{2}=(5)^{2}=25
\end{aligned}
$$
$$
\begin{aligned}
&\therefore \quad|\mathrm{A}| \mathrm{I}=5 \mathrm{I} \Rightarrow|\mathrm{A}|=5 \\
&\therefore \quad|\operatorname{adj}(\mathrm{A})|=|\mathrm{A}|^{3-1}=|\mathrm{A}|^{2}=(5)^{2}=25
\end{aligned}
$$
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