If be a permutation of degree , defined on a finite set consisting of distinct elements, by definition is a one-one mapping of onto itself. Since is one-one onto, it is invertible. Let be the inverse of map then will also be one-one map of onto itself. Thus, is also a permutation of degree on . This is known as the inverse of the permutation .

Thus if

Then

**Note:** Evidently is obtained by interchanging the rows of because etc.