Question

The least positive integer \(n\) such that \(\left(\begin{array}{rr}\cos \frac{\pi}{4} & \sin \frac{\pi}{4} \\ -\sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)^{n}\) is an identity matrix of order 2 is
(A) 4
(B) 8
(C) 12
(D) 16

Answer 1

Ans: (B)
Hint \(: A^{2}=\left(\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right), A^{4}=\left(\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right), A^{8}=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right) \therefore\) correct option is \((B)\)

Answer 2

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Answer 3

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