The emergence of novel hardware accelerators has powered the tremendous growth of machine learning in recent years. These accelerators deliver incomparable performance gains in processing high-volume matrix operators, particularly matrix multiplication, a core component of neural network training and inference. In this work, we explored opportunities of accelerating database systems using NVIDIA's Tensor Core Units (TCUs). We present TCUDB, a TCU-accelerated query engine processing a set of query operators including natural joins and group-by aggregates as matrix operators within TCUs. Matrix multiplication was considered inefficient in the past; however, this strategy has remained largely unexplored in conventional GPU-based databases, which primarily rely on vector or scalar processing. We demonstrate the significant performance gain of TCUDB in a range of real-world applications including entity matching, graph query processing, and matrix-based data analytics. TCUDB achieves up to 288x speedup compared to a baseline GPU-based query engine.