Question

Prove that permutation matrices can be expressed as a product of pairwise interchanges

Answer 1

The inverse of a permutation matrix is its transpose. If a permutation moves an element at x to y, then the inverse permutation must move y to x. In the matrix representationA permutation matrix is a matrix obtained by permuting the rows of an identity matrix according to some permutation of the numbers 1 to . Every row and column therefore contains precisely a single 1 with 0s everywhere else, and every permutation corresponds to a unique permutation matrix.

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