@Rita20, do not refund him. it's possible he's trying to scam you. Your address details were on his itinerary (sent by AirBnB), so there should be no reason he want to a wrong address. And the fact he didn't respond to your message is a flag.
Is he actually asking for a refund? If he is, instruct him to contact AirBnB.
If your communication with him was via the AirBnB site, this will leave a paper trail as well. AirBnB can then see your message that your mother was at home at the time the guest claimed to have arrived, and that you sent the guest the phone number.
Others here will likely be able to advise you as well.