Matrices are funny. You can encounter them as a teenager reading 3D graphics tutorials on the internet, learn that they can compactly represent scalings, rotations, and translations, and that several transformations can be conveniently “stacked” using this thing called matrix multiplication which looks like this… and that’s it, now you can use them for a cool practical purpose, but the tutorials never derive or attempt to justify
why mmul looks like that, often because the author doesn’t know either!
Or you can learn about them in school and be given neither a real-world use case nor a rationale or derivation for mmul.
Or you can encounter them in college, and there the experience depends on whether it’s a good or bad kind of a linalg class. But even there – after all the painstaking definitions and lemmas and derivations – it’s easy to end up not grokking how mmul does what it does even if you grasp all the building blocks – vector spaces, bases, how matrices can represent bases and systems of linear equations and linear operations on vectors and how they’re all kinda equivalent.