Why is the bi-linear bracket operation on a one-dimensional Lie algebra abelian?

[PsychonautQQ]

I just read that the bi-linear bracket operation on anyone dimensional lie algebra is abelian (vanishing) because of the anti-symmetry property. I'm not understanding the connection, can anyone enlighten me?

 

[fzero]

If the Lie algebra is one-dimensional, all of the elements are multiples of a single generator, say $L$. Any bracket is therefore proportional to $[L,L]=0$ due to antisymmetry.