We consider invertible, row diagonally dominant real matrices
and give inequalities on their minors and diagonal entries of
their inverses. A very special case is that all diagonal entries
of an inverse, of a row stochastic, row diagonally dominant
and invertible matrix, are at least 1, with strict inequality at
least when the dominance is strict. This was conjectured in
international trade theory in economics and motivated the
present work (though much more is proven). Some of the
results generalize previously known facts for M -matrices.
