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In order to meet the demands of future innovative applications, many efforts have been made to exceed the limits predicted by Shannon's Theory. Besides the investigation of beyond-Shannon metrics such as security, latency, and semantics, another direction is to jointly design the transceiver and the environment by utilizing the intelligent reflecting surface (IRS). In this paper, we consider the analysis and design of IRS-aided multiple-input multiple-output (MIMO) secure communications, which has attracted much research attention but still in its infancy. For example, despite their importance, the fundamental limits of IRS-aided wiretap MIMO communications are not yet available in the literature. In this paper, we will investigate these fundamental limits by determining the ergodic secrecy rate (ESR) and secrecy outage probability (SOP). For that purpose, the central limit theorem (CLT) for the joint distributions of the mutual information (MI) statistics over the IRS-aided MIMO secure communication channel is derived by utilizing the random matrix theory (RMT). The derived CLT is then used to obtain the closed form expressions for the ESR and SOP, which are also extended to the scenario with multiple multi-antenna eavesdroppers. Based on the theoretical results, algorithms for maximizing the artificial noise (AN) aided ESR and minimizing the SOP are proposed. Numerical results validate the accuracy of the theoretical results and effectiveness of the proposed optimization algorithms.