A) \[{{I}_{3}}\]
B) \[2{{I}_{3}}\]
C) \[4{{I}_{3}}\]
D) \[18{{I}_{3}}\]
Correct Answer: D
Solution :
We have \[A=\left[ \begin{matrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} -5 & 7 & 1 \\ 1 & -5 & 7 \\ 7 & 1 & -5 \\ \end{matrix} \right]\] \[\therefore \] \[AB=\left[ \begin{matrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \\ \end{matrix} \right]\,\,\left[ \begin{matrix} -5 & 7 & 1 \\ 1 & -5 & 7 \\ 7 & 1 & -5 \\ \end{matrix} \right]\] \[AB=\left[ \begin{matrix} 18 & 0 & 0 \\ 0 & 18 & 0 \\ 0 & 0 & 18 \\ \end{matrix} \right]=18\,\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] \[AB=18\,{{I}_{3}}\].
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