Please see some facts below:

https://math.stackexchange.com/questions/170241/when-is-matrix-multiplication-commutative

Dear Biswanath Rath,

To generate commutative matrices is a primary issue.

In fact, if A is any kxk matrix and p(x) , g(x) are any polynomials

of any order, then p(A),g(A), p(g(A)), g(p(A)),etc..all are commuting matrices.

Moreover, if A is invertible, then p(A-1),g(A-1), p(g(A-1)), g(p(A-1)), ...,p(A),g(A), p(g(A)), g(p(A)),....etc all are commuting matrices.

The obtained results are very elementary, and no new results appeared.

Notice that equations (13) and (14), (31), (32) have the forms A = aI+ M , B=bI +M, and are trivially commute, I is the identity.

This works for any dimension nxn and not only for 2x2, 3x3 matrices.

PS.

the impact factor of the mentioned Journal is not a real one.

Check (Thomson Reuters Impact Factor).

Best regards