A and B are two matrices such that $(A+B)^3=A^3+3A^2B+3AB^2+B^3$ then $ AB=BA$ Let $A$ and $B$ be two invertible matrices in $M_2(\mathbb{R})$such that $(A+B)^3=A^3+3A^2B+3AB^2+B^3$ then prove or disprove that $ AB=BA$
My working: 
$$(A+B)^3=A^3+3A^2B+3AB^2+B^3$$
$$\implies BA^2+B^2A+ABA+BAB =2A^2B+2AB^2$$
Now what should I do?

Counter-example :
$$
A=
\left(\begin{array}{cc}
2  & 0 \\
   &   \\
0 & 3 \\    
\end{array}\right),
B=
\left(\begin{array}{cc}
1  & 0 \\
   &   \\
1 & -10 \\    
\end{array}\right).
$$
