# Math Help - calculation of lie brackets

1. ## calculation of lie brackets

Hello!

We have two vectorfields on $\mathbb{R}^n$ X(x)=Ax+a, Y(x)=Bx+b, where A,B are nxn-matrices and $a, b \in \mathbb{R}^n$.

Is it true that the lie bracket [X,Y]=0?

2. What happens when you plug your vector fields into the definition of the Lie bracket?

3. Thanks for your answer. Thats what i did. I just want to be sure if my calculation is right. The lie bracket of X and Y is zero since the Hessian Matrix of a smooth function is symmetric.

Is the result correct?