Homomorphism space/Dimension/Fact

Let ${}K$ denote a field, and let ${}V$ and ${}W$ denote finite-dimensional ${}K$-vector spaces with dimensions ${}n$ and ${}m$.

Then

${}\dim _{K}{\left(\operatorname {Hom} _{K}{\left(V,W\right)}\right)}=nm\,.$

Proof, Write another proof