If A = [[2, 3], [1, 2]] and B = [[2, −3], [−1, 2]], then AB − BA equals:

If A = [[2, 3], [1, 2]] and B = [[2, −3], [−1, 2]], then AB − BA equals:

• A. [[0, 0], [0, 0]]
• B. [[1, 0], [0, 1]]
• C. [[0, 1], [−1, 0]]
• D. [[2, 3], [1, 2]]

Answer: A) [[0, 0], [0, 0]]

Explanation: AB = [[2×2+3×(−1), 2×(−3)+3×2], [1×2+2×(−1), 1×(−3)+2×2]] = [[4−3, −6+6], [2−2, −3+4]] = [[1, 0], [0, 1]]. BA = [[2×2+(−3)×1, 2×3+(−3)×2], [−1×2+2×1, −1×3+2×2]] = [[4−3, 6−6], [−2+2, −3+4]] = [[1, 0], [0, 1]]. So AB = BA = I, hence AB − BA = 0.