## 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
$\left( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 4 & 3 & 1 & 2 \end{array} \right)$