# Inverse of Permutations

If is 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 a one-one mapping 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.