Let $A = a_{i,j}$ be a positive matrix, which not all of whose rows have the same sum. Prove the the spectral radius satisfies the strict inequalities
$$\displaystyle{\min_i}\sum_{j=1}^na_{i,j}<(A)<{\max_i}\sum_{j=1}^na_{i,j}$$
How would I go about proving this? I'm not sure what the inequalities are really stating.
I know that since A is positive, then the spectral radius is an element of the spectrum of $A$, so $\rho(A) \in \mbox{spectrum}(A)$. $A$ also has an eigenvector v(i)>0 and that Av = (A). But thats really it, how do I prove these inequalities. I don't understand it and how to go about it. Thank you for your help!