Would that make things easier in any science if matrix multiplication were commutative? I mean are researchers working to find more exceptions to the general rule of matrix multiplication being not commutative? If not why?
Thank you for clearing my doubts
One famous place it matters whether your matrices are commutative is in the theory of gauge symmetries in particle physics. For electromagnetism, the "matrices" are unit complex numbers, which commute. Among other things, this makes the field equations linear. The nuclear forces can be thought of as cousins of electromagnetism that are nonlinear due to their gauge group being non-commutative.
