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An interesting theorem states the following: If a nonsingular matrix and its inverse are both nonnegative matrices (i.e. matrices with nonnegative entries), then the matrix is a generalized permutation matrix.
==Signed permutation group==
A '''signed permutation matrix''' is a generalized permutation matrix whose nonzero entries are ±1. It is the [[Coxeter group]] <math>B_n</math>, and has order <math>2^nn!</math>. It is the symmetry group of the [[hypercube]] and (dually) of the [[cross-polytope]].
==Group theory==
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