This is homework for my mathematical optimization class. Here is the exact question:
Element-wise nonnegative matrix and inverse. Suppose a matrix $A \in\Bbb R^{n\times n}$ , and its inverse $B$, have all their elements nonnegative, i.e., $A_{ij}\geq 0$, $B_{ij}\geq 0$, for $i,j = 1,\dots,n$. What can you say must be true of $A$ and $B$? Please give your answer first, and then the justification. Your solution (which includes what you can say about $A$ and $B$, as well as your justification) must be short.
I have no idea what they are looking for; so far, I've got just the basic facts stemming from the fact that an inverse exists (it's square, the determinant is non-zero etc.). What can I deduce from the "non-negative" property?