The aim of this paper is to analyze the asymptotic behavior of the eigenvalues and eigenvectors of particular sequences of products involving two square real matrices A and B, namely of the form B^kA, as k>=1. This analysis represents a detailed deepening of a particular case within a general theory on finite families F = {A_1; ... ;A_m} of real square matrices already available in the literature. The Bachmann-Landau symbols and related results are largely used and are presented in a systematic way in the final Appendix.
