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Let A be a $2 \times 2$ matrix
Statement-1 $: \operatorname{adj}(\operatorname{adj} A)=A$
Statement-2 : $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|$
Options:
Statement-1 $: \operatorname{adj}(\operatorname{adj} A)=A$
Statement-2 : $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|$
Solution:
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Verified Answer
The correct answer is:
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
$$
\begin{aligned}
& |\operatorname{adj} A|=|A|^{n-1}=|A|^{2-1}=|A| \\
& \operatorname{adj}(\operatorname{adj} A)=|A|^{n-2} A=|A|^0 A=A
\end{aligned}
$$
\begin{aligned}
& |\operatorname{adj} A|=|A|^{n-1}=|A|^{2-1}=|A| \\
& \operatorname{adj}(\operatorname{adj} A)=|A|^{n-2} A=|A|^0 A=A
\end{aligned}
$$
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