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Matrix groups, also known as linear groups, consist of matrices that form a group under matrix multiplication. They are fundamental objects of study in group theory and have wide-ranging applications in mathematics and science. In particular, matrix groups arise naturally in the study of symmetry and transformation properties of geometric objects, making them an essential tool in fields such as physics and computer graphics. The elements of a matrix group can be thought of as linear transformations that preserve certain structures or properties, such as length or orientation, leading to important subclasses of matrix groups like orthogonal and unitary groups. Matrix groups also play a central role in representation theory, where they provide a powerful framework for understanding abstract algebraic structures in terms of concrete linear maps. Overall, matrix groups offer a rich and fascinating area of study that connects group theory to a wide variety of mathematical and scientific contexts.