Practice question · Multiple choice
Matrix multiplication requires the inner dimensions to agree, and is generally not . What do both facts reflect about what a matrix product IS?
Hints
- Read from the right: which map acts first?
- Ask why the inner dimensions in particular have to match.
Show the answer
A. That it composes two transformations in a fixed order
Why
The product is composition of maps. The dimension rule says the first map’s output must be the second’s input, and order matters for the same reason rotating then reflecting differs from reflecting then rotating.
Practise Matrix Product
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