We exhibit minimal bases of the polynomial identities for the matrix algebra M-2(K) of order two over an infinite field K of characteristic p not equal 2. We show that when p = 3 the T-ideal of this algebra is generated by three independent identities, and when p > 3 one needs only two identities: the standard identity of degree four and the Hall identity. Note that the same holds when the base field is of characteristic 0. Furthermore, using the exact form of the basis of the identities for M-2(K) we give finite minimal set of generators of the T-space of the central polynomials for the algebra M-2(K). The set of generators depends on the characteristic of the field as well. (C) 2003 Elsevier Inc. All rights reserved.3775367