I am looking at proofs of the associativity of matrix multiplication. The standard proof that I have in my text book is similar to the one found here. While I do understand the proof I would have a hard time recreating it, say in an exam. However, since each matrix corresponds to a linear transformation and matrix multiplication corresponds to composition of said transformations it seems like proving associativity of composition (Which is trivial) is a sufficient proof. thoughts?
2026-03-25 17:38:34.1774460314
proving matrix multiplication associativity by viewing them as linear maps
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Absolutely yes, and this line of thought leads to extremely clear proofs. You have to just once prove a handful of properties to set up the relationship between matrices and linear transformations, and you're good to go. Do note though that the difficulty with establishing associativity becomes the proof that matrix multiplication indeed corresponds to composition. So some persistence of difficulty remains. I find it very unfortunate that so many books do not emphasize the linear transformations approach.