Lately, I´ve been struggling with math homework and came across a question I´m not sure how to answer. I will be glad for any help...
Suppose we have matrix $A$ (size $n\times n$) and its inverse (lets call it $B$). They are both non-negative in the sense that all their elements $A_{ij}$ and $B_{ij}\geq 0$, where $1\leq i,j\leq n$.
The question is, what can we say about these matrices - everything must be justified.
This where I got so far: 1) $A$ is regular (otherwise it wouldn't have and inverse - I don't think I have to justify this statement)
Are there any other features? I think I can justify some of them by using minor matrices, but I'm not sure how :-(