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In this paper, we investigate the performance of a single-relay assisted cooperative link, where the source, relay, and destination terminals are equipped with multiple transmit and receive antennas. We focus on the so-called transparent amplify-and-forward (T-AaF) for MIMO relay channels, in which the relay requires neither channel state information (CSI) nor synchronization of symbols or carrier. Specifically, we propose and analyze new selection schemes, where the relay, based on the received signal energies, selects the "best" received signal on the S → R hop and forwards it to the destination terminal with either repetitive or selective transmission. Through the derivation of pairwise error probability (PEP) expressions and asymptotic order of diversity (AOD) analysis, we demonstrate that the proposed selection schemes preserve full diversity order, while maintaining low complexity implementation, which makes them attractive from a practical point of view. Furthermore, we show that adopting selective transmission on the R → D hop provides better performance, better throughput, and significantly better energy efficiency than repetitive transmission. A Monte Carlo simulation study is also presented to corroborate the analytical results and to provide detailed performance comparisons between the two schemes under consideration.