The set of papers [3,4,6,7] (Chattopadhyay et al., 1999; Dihidar and Choudhury, 2004; Khan et al., 1997, 1999) deals with the behavior of the uniform two-dimensional cellular automata over binary fields (Z(2)). Some structural properties and precise mathematical models using matrix algebra over the field Z(2) are reported for characterizing the behavior of two-dimensional nearest neighborhood linear cellular automata with null and periodic boundary conditions [3,4,6,7] (Chattopadhyay et al., 1999; Dihidar and Choudhury, 2004; Khan et al., 1997, 1999). In this paper, we characterize two-dimensional linear cellular automata transformations by using matrix algebra built on Z(3). We analyze some results for two-dimensional CA with rule numbers 2460N and 2460P. Finally, we investigate the dimension of the kernel of two-dimensional cellular automata defined by the rule number 2460N. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.