Product with Degenerate Linear Transformation is Degenerate

Theorem
Let $U, V, W$ be vector spaces over a field $K$.

Let $G: U \to V$ be a degenerate linear transformation.

Let $N: W \to U$ be a linear transformation.

Then $G \circ N$ is degenerate.

Proof
Recall that the dimension of subspace is not greater than its super space.

Thus the claim follows from:
 * $\Img {G \circ N} \subseteq \Img G$