Finite Symmetric Group is Ambivalent

Theorem

Let $n$ be a natural number.

Let $S_n$ be a symmetric group of order $n$.

Then $S_n$ is ambivalent.

Proof

The Conjugacy Classes of Symmetric Group are determined uniquely by the cycle type of the elements.

Since any element in $S_n$ is of the same cycle type with its inverse, they are in the same conjugacy class.

Hence they are conjugates of each other.

This implies that $S_n$ is ambivalent.

$\blacksquare$