A) \[0\]
B) \[-H\]
C) \[{{H}^{2}}\]
D) \[H\]
Correct Answer: D
Solution :
\[{{H}^{2}}=\left[ \begin{matrix} \omega & 0 \\ 0 & \omega \\ \end{matrix} \right]\left[ \begin{matrix} \omega & 0 \\ 0 & \omega \\ \end{matrix} \right]=\left[ \begin{matrix} {{\omega }^{2}} & 0 \\ 0 & {{\omega }^{2}} \\ \end{matrix} \right]\] If \[{{H}^{k}}=\left[ \begin{matrix} \omega k & 0 \\ 0 & \omega k \\ \end{matrix} \right],\] So by mathematical induction, \[{{H}^{70}}=\left[ \begin{matrix} {{\omega }^{70}} & 0 \\ 0 & {{\omega }^{70}} \\ \end{matrix} \right]=\left[ \begin{matrix} \omega & 0 \\ 0 & \omega \\ \end{matrix} \right]=H\]
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