WBJEE · Maths · Matrices
The least positive integer \(n\) such that \(\left(\begin{array}{cc}\cos \frac{\pi}{4} & \sin \frac{\pi}{4} \\ -\sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)^{n}\) is an identity matrix of order 2 is
- A 4
- B 8
- C 12
- D 16
Answer & Solution
Correct Answer
(B) 8
Step-by-step Solution
Detailed explanation
We have, \(\left(\begin{array}{cc}\cos \pi / 4 & \sin \pi / 4 \\ -\sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)^{n}\) Let \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}}\end{array}\right)\)…
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