Practice question · Multiple choice
Matrix multiplication is defined by that awkward row-times-column rule rather than entry-by-entry. Why choose the complicated definition?
Hints
- Ask what a matrix is for. What operation on those objects would you most want the product to mean?
- Entry-by-entry multiplication exists and has a name. Ask what it is used for.
Show the answer
A. Because it is the rule that makes the product represent composition
Why
The definition is reverse-engineered from what it must do: apply B, then A, and the row-column rule is exactly what makes that work. Entry-by-entry multiplication is a real operation, the Hadamard product, and it is used where matrices hold data rather than transformations. The rule follows the meaning.
Practise Matrices and Matrix Operations
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