Let $A = \begin{pmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{pmatrix}$ …

Mathematics

Problem

Let

A = \begin{pmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{pmatrix}

(\alpha \in \mathbb{R})

such that

A^{32} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}

. Then a value of

\alpha

is (1)

\frac{\pi}{16}

(2) 0 (3)

\frac{\pi}{32}

(4)

\frac{\pi}{64}