How to prove my girlfriend that I am not cheating on her?

ok well I have been dating my girlfriend for a month. there's stupid rumors about me cheating on her. she believes it because she has been telling her friends that I am cheating on her. how can I prove to her that I am not cheating on her? I tried tellnig her that I'm not but she beleives that I am.
How to prove my girlfriend that I am not cheating on her?
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