The space of all linear maps from $U\to V$ is isomorphic to $\text{Mat}_{l\times k}(K).$

While trying to solve the following problem

Let $$K$$ be a finite field of $$q$$ elements. Let $$U$$, $$V$$ be vector spaces over $$K$$ with $$\dim(U) = k$$, $$\dim(V) = l$$. How many linear maps $$U \rightarrow V$$ are there?

I came across the following claim here:

The space of all linear maps from $$U\to V$$ is isomorphic to $$\text{Mat}_{l\times k}(K).$$

Could someone link me to a proof of this result?