We introduce the notions of matrix–valued wavelet set and matrix–valued multiresolution analysis (A-MMRA) associated with a fixed dilation given by an expansive linear map A: Rd→ Rd, d≥ 1 such that A (Zd)⊂ Zd, in a matrix–valued function space L2 (Rd, Cn× n), n≥ 1. These are generalizations of the corresponding notions defined by Xia and Suter in 1996 for the case where d= 1 and A is the dyadic dilation. We show several properties of orthonormal sequences of translates by integers of matrix–valued functions, focusing on those related to the structure of A-MMRA’s and their connection with matrix–valued wavelet sets. Further, we present a strategy for constructing matrix–valued wavelet sets from a given A-MMRA and, in addition, we characterize those matrix–valued wavelet sets which may be built from an A-MMRA.