Matrix Representation of the Permutation Group

The set of all permutations of forms a group under the multiplication (composition) of permutations; that is, it meets the requirements of closure, existence of identity and inverses, and associativity. We can set up a bijection between and a set of binary matrices (the permutation matrices) that preserves this structure under the operation of matrix multiplication. The bijection associates the permutation with the matrix , with zeros everywhere except for ones at row, column , for .


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