Good, intuitive introduction to matrices. Next steps could be showing that there are infinitely many different matrix representations of a linear map (different from the polynomials) and they can be used for function spaces, too.

One question that usually pops up that I was confused about till recently: are rank two tensor equivalent to matrices? Answer is no, e.g. see here: https://physics.stackexchange.com/questions/20437/are-matric...