I have a matrix $A = I + G$ where $G_{ii} = 0$ for all $i$, and $G_{ij} \in \{0, a\}$ with $a \in [0, 1[$, $G$ is symmetric, and such that $A$ is positive definite.
We know that the inverse of $A$, call it $B$, is also symmetric positive definite, and also that $B_{ii} > 1$ for all $i$.
My question: is it true that $B_{ii} > B_{ij}$ for all $i, j$?
Any help welcome! Thanks