# Identity Permutation

If $I$ is a permutation of degree $n$ such that $I$ replaces each element by the element itself, $I$ is called the identity permutation of degree $n$. Thus

Or

Or

is the identity permutation of degree $n$.

For example, $I = \left( {\begin{array}{*{20}{c}}1&2&3&4&5&6&7&8 \\ 1&2&3&4&5&6&7&8 \end{array}} \right)$ is the identity permutation on $X = \left\{ {1,2,3,4,5,6,7,8} \right\}$