The present paper studies the asymptotic performance of dual-hop amplify-and-forward multiple-input multiple-output relay communication systems. In the corresponding setup, a relay amplifies the signal received from a source, retransmitting it towards a destination, while the direct source-destination link is absent. Ergodic achievable rates under separate decoding, along with the average bit error rate under various detection schemes are derived in the regime where the number of antennas at each terminal grows without bound. To overcome the mathematical difficulty of averaging over both channel realizations and input signals we apply large-system analysis based on the replica method from statistical physics. The validity of the large-system analysis is further verified through Monte Carlo simulations, providing particularly good accuracy at low SNR.