jee-main 2019 Q75

jee-main · India · session2_08apr_shift1 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning

Let $A = \begin{pmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{pmatrix}$, $\alpha \in R$ such that $A^{32} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Then, a value of $\alpha$ is:
(1) 0
(2) $\frac{\pi}{16}$
(3) $\frac{\pi}{64}$
(4) $\frac{\pi}{32}$

Let $A = \begin{pmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{pmatrix}$, $\alpha \in R$ such that $A^{32} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Then, a value of $\alpha$ is:\\
(1) 0\\
(2) $\frac{\pi}{16}$\\
(3) $\frac{\pi}{64}$\\
(4) $\frac{\pi}{32}$

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