The paper considers the important problem of fast computation of iterative matrix equations. Three architectures for fast implementation of Faddeev's matrix inversion algorithm are described. The recursive nature of Faddeev's algorithm is indicative of many other algorithms, based on the Cayley-Hamilton theorem. All such algorithms seem well suited to the class of orbital architectures reported by Porter and specialised herein. The architectures presented here are essentially 3-dimensional structures. They clearly demonstrate several advantages over comparable 2-dimensional structures particularly with respect to speed and I/O requirements. Besides, the presented architectures are chosen to highlight various 3-dimensional solutions and associated tradeoffs that are representative of the subject class of problems.