Practice question · Multiple choice
AB and BA are both defined for two square matrices and give different answers. Why is that the expected behaviour rather than a defect?
Hints
- A matrix is a transformation. Ask what AB means as a sequence of two of them.
- Rotate a book then flip it; now flip then rotate. Compare.
Show the answer
B. Because each product composes the operations in a different order
Why
A product is a composition, and doing two things in the other order is a different act, the algebra is simply honest about that. Expecting AB = BA is importing a habit from ordinary numbers, and it is why matrix equations must be manipulated with the side of multiplication tracked.
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