Linear Transformation Maps Zero Vector to Zero Vector

Theorem
Let $\mathbf V$ be a vector space, with zero $\mathbf 0$.

Likewise let $\mathbf V\,'$ be another vector space, with zero $\mathbf 0'$.

Let $T: \mathbf V \to \mathbf V\,'$ be a linear transformation.

Then:
 * $T: \mathbf 0 \mapsto \mathbf 0'$