Facts No One Really Checks (2012)

What a strange statement/article. I had to check all three of those as an undergrad, associativity of matrix multiplication was definitely first year linear algebra, and I think elliptic curve product was first year number theory.

(and it still is, theorem 3.4 in these first year notes https://wwwf.imperial.ac.uk/~kb514/M1GLA.pdf)

"It is that they are felt too tedious or technical to prove in a course or even a textbook." Was my degree unusually tedious?

A lot of matrix concepts sound a lot more natural to me if I first think of what they mean in terms of vector spaces.

For example, I think one can derive associativity of matrix multiplication less tediously from the observation that every matrix corresponds to a linear transform from a vector space to another, multiplication corresponds to function composition, and function composition is associative.