My question follows from https://math.stackexchange.com/questions/3857976/inverse-inequality-of-symmetric-matrix. Suppose we assume that $A$ and $B$ are two positive definite matrices with positive entries and $A\geq B $ entry wise.
Can we say that $A^{-1}\leq B^{-1}$ entry wise?
I tried with numeric examples in Matlab, but I am not getting any counter-example. Any help would be really great.