Definition - An entry wise non-negative matrix is said to be ID if $A^{or} = [a_{ij}^r]$ is PSD (positive semi definite) for all $r \geq 0$ i.e r being a non-negative real no.
I need to prove or disprove that :
If A and B are ID matrices \
a ) then A+B is an ID matrix
b) and if AB = BA(so that AB becomes hermitian) then AB is also ID.
I have some example of ID matrices which are min(i,j), gcd(i,j), any 2-square PSD matrix etc. After taking these examples it seems the result is positive. Any help? Thanks in advance.