Let $A,B,C$ be square matrices. Calculate $(A+B+C)^3$ 
Let $A,B,C$ be square matrices. Calculate $(A+B+C)^3$

I used the fact that
$$(A+B+C)^2=A^2+AB+AC+BA+B^2+BC+CA+CB+C^2$$
and multiply this with $(A+B+C)$ and I got
$$A^3+A^2B+A^2C
+ABA+AB^2+ABC
+ACA+ACB+AC^2
+BA^2+BAB+BAC
+B^2A+B^3+B^2C
+BCA+BCB+BC^2
+CA^2+CAB+CAC
+CBA+CB^2+CBC
+C^2A+C^2B+C^3$$
I want to simplify this and my question is the terms $AB$ and $BA$ equal so I can add them to be $2AB$ or not necessary since the $A$ and $B$ are matrices. Thanks

The Binomial and multinomials work as usual only for commutative matrices. So this trinomial can be simplifies only if $AB=BA$,~ $BC=CB$ and $CA=AC$.
