Regardless of a measurement space or a topological space, after two consecutive mappings composite, their entropy is correlated to the composite order, however, when some conditions are met, some of composite orders can be exchanged but the entropy keeps constant after the orders are exchanged. This paper reviews in detail the definitions related to the entropy, and discusses the commutativity of the metric entropy after the composite of two mappings, metric sequence entropy, topological entropy, topological sequence entropy, topological entropy of twodimensional mapping, rotational entropy and topological pressure.