Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Let K be an infinite integral domain, and let A = M(2)(K) be the matrix algebra of order two over K. The algebra A can be given a natural Z(2)-grading by assuming that the diagonal matrices are the 0-component while the off-diagonal ones form the 1-component. In this paper we study the graded identities and the graded central polynomials of A. We exhibit finite bases for these graded identities and central polynomials. It turns out that the behavior of the graded identities and central polynomials in the case under consideration is much like that in the case when K is an infinite field of characteristic 0 or p > 2. Our proofs are characteristic-free so they work when K is an infinite field, char K = 2. Thus we describe finite bases of the graded identities and graded central polynomials for M(2)(K) in this case as well.1573247256Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FINATECConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [620025/2006-9, 302655/2005-0]FAPESP [05/60337-2]