# 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.

• what do you mean by positive matrix ? do you know hadamard lemma ? – Gabriel Romon Apr 23 '13 at 16:41
• Here positive matrix is a square matrix whose all entries are positive. – Sujeet Apr 23 '13 at 17:14

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