i am having trouble with this problem so any help would be appreciated!

A dominance digraph is one with no loops in which, for any two distinct vertices Pi and Pj, there is either an edge from Pi to Pj or an edge from Pj to Pi, but not both.

Suppose that A is a square matrix with each entry equal to 0 or to 1. Prove that A is the adjacency matrix for a dominance digraph if and only if A + the transposition of A has all main diagonal entries equal to 0, and all other entries equal to 1.