Generally speaking, operation refers to algebraic operation, which is the correspondence in a set. For ordered element pairs A and B in set A, there is a unique third element C corresponding to it in set A, which is called the operation defined in set A..

From this operation, we can get two operations, that is, one of A and B is expected and C is known. The operation thus obtained is called the inverse operation of the original operation. Its first inverse operation is: for element pairs c and b, make element a correspond to them; Its second inverse operation is to make element B correspond to element pair C and A..

If an operation satisfies the commutative law, that is, for any pair of elements A, B or B, A always gets the same result, then the two inverse operations of this operation are consistent. That is to say, in this case, this operation has a unique inverse operation.

For example, for a set of integers, the addition operation of any two integers satisfies the additive commutative law, so the addition has the only inverse operation-subtraction. Another example is that the multiplication operation of any two integers satisfies the multiplication commutative law, then the multiplication has the only inverse operation-division.

However, not every operation has an inverse operation. For example, in the set of natural numbers, the addition of natural numbers is defined, and its inverse operation-subtraction can not always be performed on any two natural numbers A and B.