In mathematics, we will sometimes employ operators to simplify the calculation process. However, are operators commutative in all situations? In fact, operators aren’t commutative in some situations. We need to consider the properties of operators and functions, or we may lead to the wrong result. In this poster, we listed eight cases. Although the operators in most of the cases are not commutative, the operators are commutative in the specific conditions. Our interest is to study the commutative properties of two operators. Eight cases are shown here.