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NDA 2 2025 Maths, question 39

Topic: Matrices and determinants

Passage · Q39 to Q40

Let A=[cos⁡θsin⁡θ−sin⁡θcos⁡θ]A=\begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}

Q39

What is the value of the determinant of the matrix A4A^{4}?

  1. (a) 00
  2. (b) 11Correct answer
  3. (c) cos⁡4θ−sin⁡4θ\cos 4\theta-\sin 4\theta
  4. (d) cos⁡24θ−sin⁡24θ\cos ^{2}4\theta-\sin ^{2}4\theta

Solution.

Answer: (b) 11

  1. The determinant of A is cos²θ+sin²θ=1.
  2. Therefore det(A⁴)=[det(A)]⁴=1.