If A = [[cos θ, −sin θ], [sin θ, cos θ]], then A + A' equals:

If A = [[cos θ, −sin θ], [sin θ, cos θ]], then A + A' equals:

• A. [[2cos θ, 0], [0, 2cos θ]]
• B. [[0, 0], [0, 0]]
• C. [[2cos θ, −2sin θ], [2sin θ, 2cos θ]]
• D. [[1, 0], [0, 1]]

Answer: A) [[2cos θ, 0], [0, 2cos θ]]

Explanation: A' = [[cos θ, sin θ], [−sin θ, cos θ]]. A + A' = [[cos θ+cos θ, −sin θ+sin θ], [sin θ+(−sin θ), cos θ+cos θ]] = [[2cos θ, 0], [0, 2cos θ]].