If matrix A = [[cos θ, sin θ], [−sin θ, cos θ]], then A A' is equal to:

If matrix A = [[cos θ, sin θ], [−sin θ, cos θ]], then A A' is equal to:

• A. A
• B. Zero matrix O
• C. Identity matrix I
• D. −I

Answer: C) Identity matrix I

Explanation: A' = [[cos θ, −sin θ], [sin θ, cos θ]]. Multiplying A and A' gives [[cos²θ + sin²θ, −cosθ sinθ + sinθ cosθ], [−sinθ cosθ + cosθ sinθ, sin²θ + cos²θ]] = [[1, 0], [0, 1]] = I.