#linearalgebra was my favorite subject in education, many years ago. Tastes differ of course...
This may be the first time I see an implementation in 'real' code. Your comments are impressive! Is performance very important here? I'm by no means an expert, but it seems like there are faster algorithms such as those Paolo mentioned. That may cost you more algebra-understanding sweat though. 😅 What kind of matrices do you intend to invert here?