Are you also going to fix the assertion that matrices form a group under multiplication? (They don't: not all matrices have inverses. The general linear group is what you are probably looking for.) It's a bit embarrassing that of your three examples of groups, only one is actually a group...

Sorry, again. I'm really trying my best to keep it all correct, but, I do make mistakes.

Another mistake you might want to fix:

>(like, matrix multplication isn't commutative, that means: A∗B≠B∗A when B and A are matrices)

You want to say something like "A∗B isn't necessarily equal to B∗A when B and A are matrices." Neither A∗B≠B∗A nor A∗B=B∗A are true in general when A and B are matrices.

Fixed. Thanks for telling me these things, it really helps.

The historical context was useful.