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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 $B \in \mathbb{R}^{b \times r}$?

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