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

I = \left( {\begin{array}{*{20}{c}}1&2&3& \cdots &n \\ 1&2&3& \cdots &n \end{array}} \right)

or

I = \left( {\begin{array}{*{20}{c}}{{a_1}}&{{a_2}}&{{a_3}}& \cdots &{{a_n}} \\ {{a_1}}&{{a_2}}&{{a_3}}& \cdots &{{a_n}} \end{array}} \right)

or

I = \left( {\begin{array}{*{20}{c}}{{b_1}}&{{b_2}}&{{b_3}}& \cdots &{{b_n}} \\ {{b_1}}&{{b_2}}&{{b_3}}& \cdots &{{b_n}} \end{array}} \right)

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 of X = \left\{ {1,2,3,4,5,6,7,8} \right\}