A) \[\left[ \begin{align} & \begin{matrix} 5 & 1 & 4 \\ \end{matrix} \\ & \begin{matrix} 2 & 6 & 3 \\ \end{matrix} \\ \end{align} \right]\]
B) \[\left[ \begin{align} & \begin{matrix} 2 & 6 & 3 \\ \end{matrix} \\ & \begin{matrix} 5 & 1 & 4 \\ \end{matrix} \\ \end{align} \right]\]
C) \[\left[ \begin{align} & \begin{matrix} 5 & 2 \\ \end{matrix} \\ & \begin{matrix} 1 & 6 \\ \end{matrix} \\ & \begin{matrix} 4 & 3 \\ \end{matrix} \\ \end{align} \right]\]
D) \[\left[ \begin{align} & \begin{matrix} 2 & 5 \\ \end{matrix} \\ & \begin{matrix} 6 & 1 \\ \end{matrix} \\ & \begin{matrix} 3 & 4 \\ \end{matrix} \\ \end{align} \right]\]
Correct Answer: C
Solution :
[c] \[A=\left[ \begin{matrix} 5 & 6 & 1 \\ 2 & -1 & 5 \\ \end{matrix} \right]\] and let \[B=\left[ \begin{matrix} 5 & 2 \\ 1 & 6 \\ 4 & 3 \\ \end{matrix} \right]\] \[\therefore AB=\left[ \begin{matrix} 5 & 6 & 1 \\ 2 & -1 & 5 \\ \end{matrix} \right]\left[ \begin{matrix} 5 & 2 \\ 1 & 6 \\ 4 & 3 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} 25+6+4 & 10+36+3 \\ 10-1+20 & 4-6+15 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} 35 & 49 \\ 29 & 13 \\ \end{matrix} \right]\]
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