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For the matrix A = [0 −1; 1 0], what is the value of A^16?

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

Correct answer: [0 1; 1 0]

Solution

The matrix A represents a 90-degree rotation in the counterclockwise direction. Since A^4 results in the identity matrix, A^16, which is A raised to the power of 4 four times, results in a 90-degree rotation four times, leading to a 180-degree rotation, represented by the matrix [0 1; 1 0].

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