Is The Matrix abelian?

Excuse me, but I'm curious to know if you've given any thought to the question, "Is The Matrix abelian?" It's an intriguing concept to ponder, especially when considering the mathematical underpinnings of the film's universe. An abelian group, as you know, is one in which the order of operations doesn't affect the result. So, when we think about the way the Matrix operates, could it be said to exhibit abelian properties? I'm genuinely interested in your thoughts on this matter.