Proving linear transformation maps 0 to 0

*Suppose that T : V -> W is linear. Prove that T(***0**) = **0**.

Not sure how I'm supposed to prove this. I know that transformations are supposed to preserve the zero vector, but I can never get my head around proving these things. I'm guessing it has something to do with preserving scalar multiplication and vector addition? What should I do?

Thanks.

Re: Proving linear transformation maps 0 to 0

Re: Proving linear transformation maps 0 to 0

Another way: $\displaystyle T(\vec{0})=T(0\cdot\vec{0})=\ldots$ .