Nonnegative matrices whose inverses are $M$-matrices
Thomas L. Markham · Proceedings of the American Mathematical Society · 1972
A characterization of a class of totally nonnegative matrices whose inverses are M-matrices is given. It is then shown that if A is nonnegative of order n and ${A^{ - 1}}$ is an M-matrix, then the almost principal minors of A of all orders are nonnegative.