\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 \(-v\) \(\blacksquare\).

\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 \(-v\) \(\blacksquare\).