Given that full duplex (FD) and MIMO both employ multiple antenna resources, an important question that arises is how to make the choice between MIMO and FD? We show that optimal performance requires a combination of both to be used. Hence, we present the design and implementation of MIDU, the first MIMO full duplex system for wireless networks. MIDU employs antenna cancellation with symmetric placement of transmit and receive antennas as its primary RF cancellation technique. We show that MIDU's design provides large amounts of self-interference cancellation with several key advantages: (i) It allows for two stages of additive antenna cancellation in tandem, to yield as high as 45 dB self-interference suppression; (ii) It can potentially eliminate the need for other forms of analog cancellation, thereby avoiding the need for variable attenuator and delays; (iii) It easily scales to MIMO systems, therefore enabling the coexistence of MIMO and full duplex. We implemented MIDU on the WARP FPGA platform, and evaluated its performance against half duplex (HD)- MIMO. Our results reveal that, with the same number of RF chains, MIDU can potentially double the throughput achieved by half duplex MIMO in a single link; and provide median gains of at least 20% even in single cell scenarios, where full duplex encounters inter-client interference. Based on key insights from our results, we also highlight how to efficiently enable scheduling for a MIDU node.