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Intelligent reflecting surface (IRS) is a new promising technology that is able to manipulate the wireless propagation channel via smart and controllable signal reflection. In this paper, we investigate the capacity region of a multiple access channel (MAC) with two users sending independent messages to an access point (AP), aided by $M$ IRS reflecting elements. We consider two practical IRS deployment strategies that lead to different user-AP effective channels, namely, the distributed deployment where the $M$ reflecting elements form two IRSs, each deployed in the vicinity of one user, versus the centralized deployment where all the $M$ reflecting elements are deployed in the vicinity of the AP. For the distributed deployment, we derive the capacity region in closed-form; while for the centralized deployment, we derive a capacity region outer bound and propose an efficient rate-profile based method to characterize an achievable rate region (or capacity region inner bound). Furthermore, we compare the capacity regions of the two cases and draw useful insights into the optimal deployment of IRS in practical systems.