# InversePermutation

InversePermutation[perm]

returns the inverse of permutation perm.

# Details • The product of a permutation with its inverse gives the identity permutation.
• Every permutation has a uniquely defined inverse.
• The support of a permutation is the same as the support of its inverse.

# Examples

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## Basic Examples(2)

Inverse of a permutation:

Their product gives the identity permutation:

Some permutations, called involutions, are their own inverse:

## Scope(1)

Invert a permutation:

## Generalizations & Extensions(1)

On symbolic expressions other than permutations the result is given in terms of PermutationPower:

## Properties & Relations(4)

InversePermutation is equivalent to PermutationPower with exponent -1:

Inverting a permutation is equivalent to reversing its cycles:

For a permutation of finite degree, its inverse can always be obtained as the power with a positive integer:

Ordering gives the inverse of a permutation list:

Introduced in 2010
(8.0)