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For the matrix A = [0 −1; 1 0], what is the value of A¹⁶?

1. [0 −1; 1 0]
2. [0 1; 1 0]
3. [−1 0; 0 1]
4. [1 0; 0 1]

Correct answer: [1 0; 0 1]

Solution

A = [[0,-1],[1,0]] rotates by 90 degrees, so A^4 = I. Since 16 = 4*4, A^16 = I = [[1,0],[0,1]].

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