Question related to diagonally dominant matrix A matrix is said to be positive if each entry in the matrix is positive.
If $A$ is real, irreducible, diagonally dominant (or strictly dominant matrix) and has positive diagonal and non-positive off-diagonal elements. Then how to show that inverse of $A$ exists and is positive.?
I am able to show that inverse of $A$ exists, but don't know how to prove that it is positive. 

I'm not sure your problem is formulated correctly. Consider $\left( \begin{array}{cc}
1 & -1  \\
-1 & 1 \end{array} \right)$.
