Non-orthogonal multiple access (NOMA) has been shown in the literature to have a better performance than OMA in terms of sum channel capacity; however, the capacity superiority of NOMA over OMA has been only proved for single antenna systems, and the proof for the capacity superiority of multiple-input multiple-output NOMA (MIMO-NOMA) over conventional MIMO-OMA has not been available yet. In this paper, we will provide our proof to demonstrate that the MIMO-NOMA is strictly better than MIMO-OMA in terms of sum channel capacity (except for the case where only one user is being communicated to), i.e., for any rate pair achieved by MIMO-OMA, there is a power split for which MIMO-NOMA can achieve rate pairs that are strictly larger. Based on this result, we prove that the MIMO-NOMA can also achieve a larger sum ergodic capacity than MIMO-OMA. Our analytical results are verified by simulations.