Advances in deep learning and neural networks have resulted in rapid development of hardware accelerators that support them. A large majority of ASIC accelerators, however, target a single hardware design point to accelerate the main computational kernels of deep neural networks such as convolutions or matrix multiplication. On the other hand, the spectrum of use-cases for neural network accelerators, ranging from edge devices to cloud, presents a prime opportunity for agile hardware design and generator methodologies. We present Gemmini1 - an open source and agile systolic array generator enabling systematic evaluations of deep-learning architectures. Gemmini generates a custom ASIC accelerator for matrix multiplication based on a systolic array architecture, complete with additional functions for neural network inference. Gemmini runs with the RISC-V ISA, and is integrated with the Rocket Chip System-on-Chip generator ecosystem, including Rocket in-order cores and BOOM out-of-order cores. Through an elaborate design space exploration case study, this work demonstrates the selection processes of various parameters for the use-case of inference on edge devices. Selected design points achieve two to three orders of magnitude speedup in deep neural network inference compared to the baseline execution on a host processor. Gemmini-generated accelerators were used in the fabrication of test systems-on-chip in TSMC 16nm and Intel 22FFL process technologies.