In this paper, we consider a point to point full duplex (FD) MIMO communication system. We assume that each node is equipped with an arbitrary number of antennas which can be used for transmission or reception. With FD radios, bidirectional information exchange between two nodes can be achieved at the same time. In this paper we design bidirectional link selection schemes by selecting a pair of transmit and receive antenna at both ends for communications in each direction to maximize the weighted sum rate or minimize the weighted sum symbol error rate (SER). The optimal selection schemes require exhaustive search, so they are highly complex. To tackle this problem, we propose a Serial-Max selection algorithm, which approaches the exhaustive search methods with much lower complexity. In the Serial-Max method, the antenna pairs with maximum "obtainable SINR" at both ends are selected in a two-step serial way. The performance of the proposed Serial-Max method is analyzed, and the closed-form expressions of the average weighted sum rate and the weighted sum SER are derived. The analysis is validated by simulations. Both analytical and simulation results show that as the number of antennas increases, the Serial-Max method approaches the performance of the exhaustive-search schemes in terms of sum rate and sum SER.