(0, 1)-Matrices with Isomorphic Term Bigraphs have Equal Ranks

Let M = || m_ij || be a (0, l)-matrix of order m x n. The term bigraph T(M) of M is the graph whose vertex set is the union of two disjoint sets V = {V₁,..., V_m) and W = {w₁,..., w_n} and in which the vertices v_i, w_j (1 ≤ i ≤ m, 1 ≤ j ≤ n) are adjacent if and only if m_ij = 1, while neither any two vertices of V, nor any two vertices of W are joined together by an edge.