A) dig (5, 4, 11)
B) dig (-4, 3, 18)
C) dig (3, 1, 8 )
D) B
Correct Answer: B
Solution :
\[{{A}^{2}}B=(A.\,A)B=\left[ \begin{matrix} 2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 3 \\ \end{matrix} \right]\,\left[ \begin{matrix} 2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 3 \\ \end{matrix} \right].\,\left[ \begin{matrix} -1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} 4 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 9 \\ \end{matrix} \right]\,\left[ \begin{matrix} -1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2 \\ \end{matrix} \right]=\left[ \begin{matrix} -4 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 18 \\ \end{matrix} \right]\].
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