Matrix multiplication units (MMUs) in modern parallel processors enable efficient execution of tiled matrix multiplications at varying precisions. While their effectiveness in AI workloads has been well demonstrated, their utility in scientific computing lacks systematic analysis. In this work, we characterize MMUs across a broad range of scientific computing patterns by evaluating performance, power consumption, numerical precision, and memory access behavior. To support this analysis, we develop Cubie, a comprehensive benchmark suite comprising ten MMU-optimized kernels of key parallel patterns. We also categorize MMU utilization patterns into four quadrants and identify the MMU limitations that arise in scientific computing. Through detailed comparisons with vector units, we provide nine key observations on the behavior and implications of MMUs in general scientific workloads, offering valuable insights for architecture, algorithm, and application researchers.