Matrix Rings

Matrix rings are mathematical structures composed of square arrays of numbers, called matrices, which can be added and multiplied following specific rules. In this context, the set of all matrices of a given size forms a "ring," meaning they are closed under these operations and satisfy properties like associativity and the existence of additive identity (a zero matrix). Matrix rings are fundamental in linear algebra, enabling us to analyze systems of equations, transformations, and more, by providing a structured framework to manipulate and study matrices systematically.