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NDA 2025 · PYQ · Matrices · easy

If f(θ) = [cosθ sinθ; -sinθ cosθ], then what is {f(π)}² equal to?

Answer

The correct answer is D: [1 0; 0 1]. f(θ) is a rotation matrix. f(π)² = f(2π) = [cos2π sin2π; -sin2π cos2π] = [1 0; 0 1] = identity matrix.

  1. A.[-1 0; 0 -1]
  2. B.[1 1; 1 1]
  3. C.[-1 0; 0 1]
  4. D.[1 0; 0 1]✓ Correct

Explanation

f(θ) is a rotation matrix. f(π)² = f(2π) = [cos2π sin2π; -sin2π cos2π] = [1 0; 0 1] = identity matrix.
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