an old result of L. Kronecker on pairs of matrices can be used effectively in the classification, but over algebraically closed fields. This result of L. Kronecker on pairs of matrices was actually a completion of the work of K. Weierstrass. Then later on I. M. Gelfand and V. Ponomarev [@Gel-Pon] observed in their analysis of the representations of the Lorentz group that quiver techniques were quite useful and they both knew that G.Szekeres had a result in this direction. However, they did not know enough details about Szekeres’s techniques and therefore they invented their new innovative and influencial quiver method which is influenced by Maclane’s notion of relations – a generalization of a linear map. In [@hell-rei] A. Heller and I. Reiner provided another nice approach to the classification where they also worked over fields that are not necessarily algebraically closed. Finally D. Benson [@ben-1] wrote a modern treatment of the classification of the indecomposable representations of the Klein group in which he combined some of the crucial ideas in the works of the aforementioned people. The diagrammatic methods in our paper are inspired by S. B. Conlon who introduced these in [@conlon]. It is quite remarkable that a 