A Matrix
obtained by permuting the th and th rows of the Identity Matrix with .
Every row and column therefore contain precisely a single 1, and every permutation corresponds to a unique permutation
matrix. The matrix is nonsingular, so the Determinant is always Nonzero. It satisfies

where

Interpreting the 1s in an permutation matrix as Rooks gives an allowable configuration of nonattacking Rooks on an Chessboard.

© 1996-9

1999-05-26