Great indication of the power of linear algebra! One little nitpick: not all transformations can be expressed with matrices, only the linear ones. Once you homogenize, you can get the affine ones (like linear, but allowing for translation, so that you don't need to respect a fixed origin). However, you can't, at least not without considerable violence to your coordinate system, express a transformation that, e.g., scales distances quadratically instead of linearly. Fortunately, as you suggest, this doesn't seem to be a transformation that's needed a lot in routine graphical editing.

Also, if you wanted to, you could juice up your discussion of the importance of performing transformations in the right order to introduce the idea of conjugates (https://en.m.wikipedia.org/wiki/Inner_automorphism) and commutators (https://en.m.wikipedia.org/wiki/Commutator). Although in your context introducing these explicitly might just make the exposition more complicated, they are useful tools to have in your general toolkit. (Conjugacy in particular, as you implicitly discuss, is practically built to express the idea "change from inconvenient coordinates to convenient ones, transform in convenient coordinates, then change back.")