Permutations as Matrices

Every permutation of a set of integers - or by extension, any set of numbers or objects, can be represented by a matrix. Specifically, a permutation of a set of  
\[n\]
  integers can be represented by a matrix with two rows and n columns.
To illustrate consider the permutation  
\[(1423)\]
. This permutation sends
1 to 4
2 to 3
3 to 1
4 to 2
We can represent this permutation as the matrix  
\[ \left( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 4 & 3 & 1 & 2 \end{array} \right) \]

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