A) \[\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 0 & 10 \\ 10 & 0 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 10 & 1 \\ 1 & 10 \\ \end{matrix} \right]\]
D) None of these
Correct Answer: A
Solution :
\[A(adj\,A)=\left[ \begin{matrix} 3 & 2 \\ 1 & 4 \\ \end{matrix} \right]\,.\,\left[ \begin{matrix} 4 & -2 \\ -1 & 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\]. Aliter: \[A\,(adj\,A)=|A|I=10\text{ }\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\].
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