In understanding groups, one must also know that it can be divided into subgroups. Her concentration was in Linear Algebra which revolves around matrices and their properties. A matrix is an array such as . The entries a, b, c, d are the elements of this matrix. They are subject to operations of addition and multiplication, which are generalizations of those on numbers.
Matrix multiplication is associative.
Matrix multiplication is distributive over addition. Matrix addition is commutative. When we commute the problem and say BA, we get . Therefore, we have shown that AB BA and thus proving matrix multiplication is not commutative. Browne used these definitions to explain classical groups and topological spaces in her article from American Mathematical Monthly , A Note on the Classical Groups.