Is it true that Luther intentionally mistranslated Romans 3:28?

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I recently listened to Dr. Scott Hahn’s conversion testimony. One thing that really jumped out at me was that Dr. Hahn stated that Luther purposely inserted the German word “allein” (alone) into Romans 3:28 despite the fact that it is not in the Greek texts.

So halten wir nun dafür, daß der Mensch gerecht werde ohne des
Gesetzes Werke, allein durch den Glauben.

Or in English literally:

Thus, we conclude that a man is justified without the deeds of the law
through faith alone.

Was it possibly a mistake, or where there other motivated factors at play?

Are there any writings from Luther that allude to his own translation of this crucial verse?

_{Note: I asked this question on C.SE (later closed as a duplicate of this question), but thought it might be more appropriate here.}