A matrix group is a collection of matrices that can be combined through matrix multiplication and addition while still remaining within the group. These groups are often studied in the field of linear algebra and are important in various areas of mathematics and physics. The matrices in a matrix group must satisfy certain properties, such as being invertible and closed under multiplication. One common example of a matrix group is the general linear group, which consists of all invertible matrices of a given size. Matrix groups can also represent symmetries and transformations in geometry and are used in applications like computer graphics and quantum mechanics. Understanding matrix groups helps in analyzing complex systems and their behaviors.