-1v=-v
\begin{align} v+(-1)v &= (1+(-1))v \\ &= 0v \\ &= 0 \end{align}
As (-1)v=0, (-1)v is the additive identity of v which we defined as -v \blacksquare.
As (-1)v=0, (-1)v is the additive identity of v which we defined as -v \blacksquare.