This paper presents an amplify-and-forward (AF) relay scheme for M-source-M-destination pairs and N relay nodes. Cooperative minimum mean square error (MMSE) and zero-forcing (ZF) strategies for wireless relay networks under the relay power constraint are investigated. The main contribution of this paper is the derivation of both the MMSE-based and the ZF-based amplifying relay matrices (ARMs) under the relay power constraint. By adopting the ARMs derived, the cost function and the total signal component power (SCP) of the received signals at the destination nodes are investigated. Finally, the system bit error rate (BER) performance is evaluated theoretically by using the cost function and total SCP behaviors, and numerically by using Monte-Carlo simulations.