If A = [[0, 1], [1, 0]] and B = [[1, 0], [0, 1]], then (AB)' equals:
If A = [[0, 1], [1, 0]] and B = [[1, 0], [0, 1]], then (AB)' equals:
- A. [[0, 1], [1, 0]]
- B. [[1, 0], [0, 1]]
- C. [[0, 0], [0, 0]]
- D. [[1, 1], [1, 1]]
Answer: A) [[0, 1], [1, 0]]
Explanation: AB = [[0×1+1×0, 0×0+1×1], [1×1+0×0, 1×0+0×1]] = [[0, 1], [1, 0]]. (AB)' = [[0, 1], [1, 0]] which equals AB itself. Note: (AB)' = B'A' = [[1, 0], [0, 1]] × [[0, 1], [1, 0]] = [[0, 1], [1, 0]].
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