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    integers can be represented by a matrix with two rows and n columns.
To illustrate consider the permutation  . This permutation sends
1 to 4
2 to 3
3 to 1
4 to 2
We can represent this permutation as the matrix