The general linear group, denoted as GL(n, F), consists of all invertible n x n matrices with entries from a field F. This group is important in linear algebra and abstract algebra because it describes all possible linear transformations that can be performed on an n-dimensional vector space over the field F. The group operation is matrix multiplication, and the identity element is the n x n identity matrix. The general linear group has various subgroups, such as the special linear group SL(n, F), which includes matrices with a determinant of 1. These groups are fundamental in many areas of mathematics, including geometry, representation theory, and the study of symmetries.