I had a quick question regarding a result that I see a lot regarding M-matrix properties, but whose proof keeps eluding me. It is stated as follows:
If A is an M-matrix, i.e. its inverse is non-negative element-wise, then the diagonal elements of A are positive. To be more specific, I would like to use inverse-positivity to prove that the first diagonal element of A is positive.
Any quick and easy ways of doing this (preferably without any theorems and the like)?