This document presents two novel techniques for Multi-Party Computation based on secret sharing where the objects of computation are square matrices over a finite field. Matrix Triples can be consumed during the evaluation phase to obtain the product of two matrices, and they have quadratic space complexity, which makes them more efficient for this purpose than ordinary multiplication triples. Matrix Power Tuples are costly to produce during the preprocessing phase but allow the parties to take a matrix to a power with just a single round of communication during the evaluation phase. The latter technique also has a considerably simpler and cheaper variant that can be applied in cases where multiplication is commutative. We provide a bottom-up explanation of the ideas behind Matrix Power Tuples, as well as a formal specification of both techniques in the form of protocols and ideal functionalities. We use the latter to provide a security proof in the iUC model. We also provide an introduction into the most widely used techniques for Multi-Party Computation in the modern literature.