On the orbits associated with the Collatz conjecture (Q2229513)

\textit{J. F. Alves} et al. [Linear Algebra Appl. 394, 277--289 (2005; Zbl 1116.11012)] proved that the existence of only one orbit associated with the so-called Collatz conjecture is equivalent to the determinant of each matrix of a certain sequence of matrices (coined as Collatz matrices) to have the same value. However, for two particular cases the problem remains open. In the paper under review, the authors discuss and solve it partially.