the dimension of the kernel of a linear transformation is equal to the dimension the kernel of its transpose: is it always true?

Question

let $V$ and $W$ be finite dimensional subspaces, let $T: V$$\to$$W$ be a linear transformation, let $T*:W*$$\to$$V*$ be its transpose, prove that $dimKerT=dimKerT*$.

I can prove they have the same rank and I know it's true if T has a square matrix, but what if it doesn't? or if it has to be square, how do I prove it?