Let G be a strongly connected and balanced directed graph. We define the resistance rij between any two vertices i and j of G by using the Moore–Penrose inverse of the Laplacian matrix of G and define the resistance matrix by R := [rij]. This generalizes the resistance in the undirected case. In this paper, we show that R is a non-negative matrix and obtain an expression to compute the inverse, determinant and cofactor sums of R. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.