This course provides an introduction to some of the more important topics in the field of Matrix Algebra. Matrix Algebra has widespread applications in the fields of Economics, Psychology and Sociology. Therefore it is essential for students majoring in any of the aforementioned fields to have a working knowledge of Matrix Algebra. This course also provides students with an excellent introduction to some of the abstract concepts that underpin much of modern mathematics. Although considerable emphasis will be placed on the computational aspects of Matrix Algebra, students will learn how to provide proofs for some of the basic algebraic facts that will be encountered during the course.