Danger: commuting adders

 

Here is a Network Rail sign at Seascale station. The adders might be a danger to commuters. As quantum physics is based on the fact that not every object is commutative under multiplication, were there any examples in which addition does not commute? Normally 3x2 = 2x3 but with matrices that need not be true under multiplication. But surely it is always true that 3+2 = 2+3. This must also work with matrices. It is clearly a question that other people are asking. I don't understand group theory well enough to fully understand this discussion.