Null Space of an Identity Transformation Let $V$ and $W$ be vector spaces and let $I: V \to V$ be the identity transformation. In _Linear Algebra_ by Friedberg, Insel and Spence, it states that the nullspace of an identity transformation is $\\{0\\}$, but I'm having a hard time seeing why, can anyone help me?

Let $N$ be the null space of $I$. Then, $N=\\{v\in V|I(v)=0\\}$. Now, note that $0=I(v)=v\iff v =0$. Hence, $N=\\{0\\}$.