Thread: calculation of lie brackets

Hello!

We have two vectorfields on X(x)=Ax+a, Y(x)=Bx+b, where A,B are nxn-matrices and .

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?

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?