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Matrix inversion is a common function found in many algorithms used in wireless communication systems. As FPGAs become an increasingly attractive platform for wireless communication, it is important to understand the tradeoffs in designing a matrix inversion core on an FPGA. This paper describes a matrix inversion core generator tool, GUSTO, that we developed to ease the design space exploration across different matrix inversion architectures. GUSTO is the first tool of its kind to provide automatic generation of a variety of general purpose matrix inversion architectures with different parameterization options. GUSTO also provides an optimized application specific architecture with an average of 59% area decrease and 3X throughput increase over its general purpose architecture. The optimized architectures generated by GUSTO provide comparable results to published matrix inversion architecture implementations, but offer the advantage of providing the designer the ability to study the tradeoffs between architectures with different design parameters.