  Recently, Cerda-Morales \cite{Ce6} introduced commutative matrices derived
from the third-order Jacobsthal matrix sequence and the third-order
Jacobsthal--Lucas matrix sequence. In the present work, through the
identification of certain special matrices, we can identify other forms of
demonstration and also the description of commutative matrix properties for
negative indices. A new generalization of this sequence is used for our
purpose.
