iran-konkur 2017 Q139

iran-konkur · Other · konkur-riazi_1396_specialized Matrices Matrix Power Computation and Application
139. If $\begin{bmatrix} \cos 15° & \sin 15° \\ -\sin 15° & \cos 15° \end{bmatrix}^n = -I$, what is the smallest natural number $n$?
(1) $6$ (2) $12$ (3) $18$ (4) $24$
\textbf{139.} If $\begin{bmatrix} \cos 15° & \sin 15° \\ -\sin 15° & \cos 15° \end{bmatrix}^n = -I$, what is the smallest natural number $n$?

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(1) $6$ \hfill (2) $12$ \hfill (3) $18$ \hfill (4) $24$

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