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== Properties ==
* 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.
* The determinant of a generalized permutation matrix is given by
:<math>\det(G)=\det(P)\cdot \det(D)=\operatorname{sgn}(\pi)\cdot d_{11}\cdot \ldots \cdot d_{nn}</math>,
where <math>\operatorname{sgn}(\pi)</math> is the sign of the permutation <math>\pi</math> associated with <math>P</math> and <math>d_{11},\ldots ,d_{nn}</math> are the diagonal elements of <math>D</math>.
== Generalizations ==
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