Group Theory Is Just a Theorem

A lot of things trickle down from group theory that most people won't really trace back to. So do properties about groups Tell us things about matrices as well like for example if you have like properties of symmetric matrics Let's say you define a symmetric matrix and no one else knows about this Is there something you can go read about group theory and say oh These should have this property because groups? I feel like it just represents Because I feel like you're the the actual use cases of it You're just mentioning how We anyways do things with it, but they're just representing What we already know Like rotating the square But this just tells us that hey when we do it it's