In this work we present some relationships between an EP matrix T, its Aluthge transform ∆(T) or the λ-Aluthge transform ∆ λ (T) and the Moore-Penrose inverse T †. We prove that the λ-Aluthge transform of T is also an EP matrix, and the same thing holds for ∆ λ (T) † and ∆ λ (T †). Also, we explore the product ∆ λ (T)T, the connections between ∆(T) and T † as well as the reverse order law for generalized inverses which are associated with ∆ λ (T). Finally, it is verified that the ranges of T and ∆ λ (T) are equal in the case of EP matrices.