AP EAMCET · Maths · Matrices
If \(A=\left[\begin{array}{cc}\cos \frac{2 \pi}{33} & \sin \frac{2 \pi}{33} \\ -\sin \frac{2 \pi}{33} & \cos \frac{2 \pi}{33}\end{array}\right]\), then \(\mathrm{A}^{2017}=\)
- A A
- B \(A^2\)
- C \(A^4\)
- D \(\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)
Answer & Solution
Correct Answer
(C) \(A^4\)
Step-by-step Solution
Detailed explanation
\(A = R\left(\frac{2\pi}{33}\right)\). \(A^{2017} = R\left(2017 \times \frac{2\pi}{33}\right) = R\left(\frac{4034\pi}{33}\right)\). \(R\left(\frac{4034\pi}{33}\right) = R\left(122\pi + \frac{8\pi}{33}\right) = R\left(\frac{8\pi}{33}\right)\).…
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