Outsourced computation can put client data confidentiality at risk. Existing solutions are either inefficient or insufficiently secure: cryptographic techniques like fully-homomorphic encryption incur significant overheads, even with hardware assistance, while the complexity of hardware-assisted trusted execution environments has been exploited to leak secret data. Recent proposals such as BliMe and OISA show how dynamic information flow tracking (DIFT) enforced in hardware can protect client data efficiently. They are designed to protect CPU-only workloads. However, many outsourced computing applications, like machine learning, make extensive use of accelerators. We address this gap with Dolma, which applies DIFT to the Gemmini matrix multiplication accelerator, efficiently guaranteeing client data confidentiality, even in the presence of malicious/vulnerable software and side channel attacks on the server. We show that accelerators can allow DIFT logic optimizations that significantly reduce area overhead compared with general-purpose processor architectures. Dolma is integrated with the BliMe framework to achieve end-to-end security guarantees. We evaluate Dolma on an FPGA using a ResNet-50 DNN model and show that it incurs low overheads for large configurations ($4.4\%$, $16.7\%$, $16.5\%$ for performance, resource usage and power, respectively, with a 32x32 configuration).