Description:  In elementary classical algebra, we have the ``commutativity'' of products, which means that when we multiply two variables, the order we multiply them does not change the result. For instance, if we have two variables x and y, then the product xy is the same as the product yx. However, for more advanced mathematical objects, there are algebras which are not commutative, and in particular, in which the order we multiply variables matters. For example, if A and B are two matrices, AB is not equal to BA in general.