If a matrix has rank r, show that there exists two matrices such that their product give initial matrix, both with rank r

Question

Let $A\in\mathcal{M}_{m,n}(\mathbb{R})$ a matrix with rank $r$. Proof that exist two matrices $B\in\mathcal{M}_{m,r}(\mathbb{R})$ and $C\in\mathcal{M}_{r,n}(\mathbb{R})$, both with rank $r$ such that $A=BC$.