In an adjacency matrix which encodes for a directed Hamiltonian path, a non-zero determinant value certifies the existence of a directed Hamiltonian path when no zero rows (columns) and no similar rows (columns) exist in the adjacency matrix

The decision version of Directed Hamiltonian path problem is an NP-complete problem which asks, given a directed graph G, does G contain a directed Hamiltonian path? In two separate papers, the author expresses the graph problem as an adjacency matrix and a proof given to show that under two special conditions relating to theorems on the determinant of a square matrix, a non-zero determinant value certifies the existence of a directed Hamiltonian path. Here, a brief note is added to repair a flaw in the proof. The result, as expressed in the paper title is a more defensible proposition.