Elementary proof for $\text{rank} \left(A \otimes B \right) = \text{rank}A\cdot \text{rank}B$

(Where $\otimes$ denotes Kronecker product) Hello, All the proofs I found for this equality are using SVD decomposition and singular values. Let $A,B\in \mathbb{F}^{n\times n}$ I want to prove the