A) \[R(s)+R(t)\]
B) \[R\,(st)\]
C) \[R(s+t)\]
D) None of these
Correct Answer: C
Solution :
\[R(s)\,R(t)=\left[ \begin{matrix} \cos s & \sin s \\ -\sin s & \cos s \\ \end{matrix} \right]\,\left[ \begin{matrix} \cos t & \sin t \\ -\sin t & \cos t \\ \end{matrix} \right]\] = \[\left[ \begin{matrix} \cos (s+t) & \sin (t+s) \\ -\sin (s+t) & \cos (t+s) \\ \end{matrix} \right]=R(s+t)\].
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