Hello!
We have two vectorfields on $\displaystyle \mathbb{R}^n$ X(x)=Ax+a, Y(x)=Bx+b, where A,B are nxn-matrices and $\displaystyle a, b \in \mathbb{R}^n$.
Is it true that the lie bracket [X,Y]=0?
What happens when you plug your vector fields into the definition of the Lie bracket?