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Q21Section DA (Data Science and Artificial Intelligence (Q11–Q65))21 of 65

High power of a 2x2 rotation matrix

Let M=(cos⁡θ−sin⁡θ sin⁡θcos⁡θ)M = \begin{pmatrix} \cos\theta & -\sin\theta \ \sin\theta & \cos\theta \end{pmatrix} be a 2×22 \times 2 matrix, where θ=2π5\theta = \frac{2\pi}{5}, and I2=(10 01)I_2 = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}. Which of the following options is equal to M2026M^{2026} ?

Options

Pick an option to check your answer. In a mock test a wrong answer here costs 1/3 mark.