Question

Question: Find the inverse of each permutation in${\mathit{S}}^{\mathbf{3}}$.

Short answer

The inverse of the permutation in are.

Step-by-step solution

Permutation

Let $\mathit{S}$be a non-empty set. A permutation on $\mathit{S}$is defined as a bijective mapping

$\mathit{f}\mathbf{:}\mathit{S}\mathbf{\to }\mathit{S}$. If, $\mathit{S}\mathbf{=}\mathbf{\{}{\mathbf{a}}_{\mathbf{1}}\mathbf{,}{\mathbf{a}}_{\mathbf{2}}\mathbf{,}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}{\mathbf{a}}_{\mathbf{n}}\mathbf{\}}$. Then, the number of bijection from $\mathit{S}$onto width="14">Sis width="17">n!Let one of the bijection be width="11">fwhich maps width="17">a'to width="36">f(ai). This is denoted by the symbol,