I don't understand what's so wrong about that. Surely the interested student would like to learn about the properties of matrix arithmetic as well as vector spaces, linear transformations and their representation as matrices, etc.

I've had a quite accomplished mathematician for a professor who was very adamant that students should learn about basic matrix operations before the abstract theory. According to him, his undergraduate education at Princeton did things the "right" way, but left him quite confused about the main ideas and motivations. He ended up making some quite important contributions to the theory of representations of some certain algebraic structures if I recall correctly.