How to show that for $a \in \mathbb{F}$, $u \in V$ that $-au=-(au)$?

Question

Suppose $V$ is an arbitrary vector space over a field $\mathbb{F}$. I am working a proof and I am almost at the result the last step I am struggling on is to show that for all $a \in \mathbb{F}$, and all $u \in V$ that $-au=-(au)$

I'm working on the LHS but I really don't know what to even do as it just seems like there isn't really any steps I can take to get it to equal the RHS without just stating it.

Any advice?

Answer 1

$au+(-a)u = (a-a)u=0u=0 \implies (-a)u=-(au)$