A) \[\left( \begin{matrix} 1 & 4 & -2 \\ -2 & 1 & 4 \\ 4 & -2 & 1 \\ \end{matrix} \right)\]
B) \[\left( \begin{matrix} 1 & -2 & 4 \\ 4 & 1 & -2 \\ -2 & 4 & 1 \\ \end{matrix} \right)\]
C) \[\left( \begin{matrix} 1 & 2 & 4 \\ -4 & 1 & 2 \\ -4 & -2 & 1 \\ \end{matrix} \right)\]
D) None of these
Correct Answer: B
Solution :
\[A=\left[ \begin{matrix} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 2 & 0 & 1 \\ \end{matrix} \right]\], \[{{A}_{11}}=1,\,{{A}_{21}}=-2,\,{{A}_{31}}=4\] \[{{A}_{12}}=4,\,{{A}_{22}}=1,\,{{A}_{32}}=-2\] \[{{A}_{13}}=-2,\,{{A}_{23}}=4,\,{{A}_{33}}=1\] \[Adj\,(A)=\left[ \begin{matrix} 1 & -2 & 4 \\ 4 & 1 & -2 \\ -2 & 4 & 1 \\ \end{matrix} \right]\].
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