# Does submultiplicative property hold for rectangle matrix in Frobenius norm?

I know $$||AB||_{F} \leq ||A||_{F}\cdot ||B||_{F}$$ when $$A,B \in \mathbb{R}^{p\times p}$$. Does this property still holds when $$A$$ and $$B$$ are rectangle matrice? For example, $$A \in \mathbb{R}^{p \times b}$$ and $$B \in \mathbb{R}^{b \times r}$$?