If $\operatorname{det}(\mathrm{AB})=(\operatorname{det} \mathrm{A})(\operatorname{det} \mathrm{B})$ and $\mathrm{A}$ is a non-singular matrix of $\operatorname{order} 3 imes 3$, then $\operatorname{det}(\operatorname{adj} A)=$

Question

If $\operatorname{det}(\mathrm{AB})=(\operatorname{det} \mathrm{A})(\operatorname{det} \mathrm{B})$ and $\mathrm{A}$ is a non-singular matrix of $\operatorname{order} 3 	imes 3$, then $\operatorname{det}(\operatorname{adj} A)=$

Aicharya · Accepted Answer

$\begin{aligned} & 	ext {Since } \operatorname{adj} A=|A| \Rightarrow|\operatorname{adj} A|=|A|^3 \ & \Rightarrow|\operatorname{adj} A|=|A|^2\end{aligned}$

If $\operatorname{det}(\mathrm{AB})=(\operatorname{det} \mathrm{A})(\operatorname{det} \mathrm{B})$ and…

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