In mathematical texts one often finds expressions like a_1, ... a_n are mutually commutative / pairwise commutative. This usually means that a_i a_j = a_j a_i for all i,j=1, ..., n. (Oft course, I assume here that these expressions have some mathematical meaning in some sense, i.e. that the products involved are defined.)

I would like to ask if there is a difference between these expressions. I know that the words mutually and pairwise have different meanings. But I do not see any mathematical difference here. Is one of them preferable? If so, why?

Best regards,

udoh