A) \[\left[ \begin{matrix} 3 & -9 & -5 \\ -4 & 1 & 3 \\ -5 & 4 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 3 & -4 & -5 \\ -9 & 1 & 4 \\ -5 & 3 & 1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -3 & \,\,4 & 5 \\ 9 & -1 & -4 \\ 5 & -3 & -1 \\ \end{matrix} \right]\]
D) None of these
Correct Answer: B
Solution :
Let, \[A=\left[ \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \\ \end{matrix} \right]\]; \[adj(A)=\left[ \begin{matrix} {{A}_{11}} & {{A}_{21}} & {{A}_{31}} \\ {{A}_{12}} & {{A}_{22}} & {{A}_{32}} \\ {{A}_{13}} & {{A}_{23}} & {{A}_{33}} \\ \end{matrix} \right]\] \[\Rightarrow \] \[{{A}_{11}}=3,\,\,{{A}_{12}}=-9,\,\,{{A}_{13}}=-5\] \[{{A}_{21}}=-4,\,{{A}_{22}}=1,\,{{A}_{23}}=3\] \[{{A}_{31}}=-5,\,{{A}_{32}}=4,\,{{A}_{33}}=1\] \[\Rightarrow \] \[Adj\,(A)=\left[ \begin{matrix} 3 & -4 & -5 \\ -9 & 1 & 4 \\ -5 & 3 & 1 \\ \end{matrix} \right]\].
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