We consider a communication network, where two mutually interfering 2-user MIMO Multiple Access Channels (MAC) operate simultaneously via the same timefrequency space, and characterize the capacity region of this network when the channel matrices satisfy a strong interference condition. This interfering MAC (IMAC) with aforementioned channel matrices is called strongly ordered IMAC in this work. We characterize the capacity region first using the genie aided approach to find out several constraints that must be satisfied by any achievable rate tuple. Then we show that independent Gaussian coding at each transmitter and joint decoding of the messages at the receivers can achieve all the rate pairs that satisfy all the aforementioned constraints. In an IMAC, there are two types of tradeoffs between rates of communication; it is between the rates of users from different MACs and among rates of users belonging to the same MAC. Result shows two tradeoffs are homogeneous.iii ACKNOWLEDGMENTS