Basically I’m wondering if the concatenation of two equal length string is context free. I’ve seen multiple proofs of this online using PDAs but we aren’t covering them in my automata course and my professor says they aren’t needed for the proof. Any help would be greatly appreciated!

This is the full question:

For any two languages $ A, B$ over $ \Sigma$ , define $ A \diamond B := \{xy\mid x \in A, y \in B, |x| = |y|\}$ . Show that if $ A, B$ are regular then $ A \diamond B$ is context-free