Abstract
The main object of this paper is to give a different approach to proof of generating matrix functions for Laguerre matrix polynomials. We also obtain the hypergeometric matrix representations, addition theorem, finite summation formula and an integral representation for Laguerre matrix polynomials. We get the relations between Laguerre, Legendre and Hermite matrix polynomials. We get the generating matrix functions for the Laguerre matrix polynomials, involving the Horn's and hypergeometric matrix functions. Finally, we define a new generalization of the Laguerre matrix polynomials with the hypergeometric matrix function.