In the present paper, we study a non-degenrate ruled surface along a null curve in a 3-dimensional Minkowski space E31, which is called a null scroll, an investigate some characterizations of null scrolls satisfying the condition H=AH, A Mat(3, ), where denotes the Laplacian of the surface with respect to the induced metric, H the mean curvature vector and Mat(3, ) the set of 3$ imes$3-real matrices.