### Abstract

‘Matrices and groups’ continues with the example of geometric matrix products to see what happens when we compose the mappings involved. It explains several features, including the identity matrix, the inverse matrix, the square matrix, and the concept of isomorphism. If a collection of matrices represent the elements of a group, such as the eight matrices that represent the dihedral group *D*, then each of these matrices *A* will have an inverse, *A*^{−1}, such that *AA ^{-1} = A^{-1}A =I*, the identity matrix. This prompts the twin questions of when the inverse of a square matrix

*A*exists and, if it does, how to find it.