Does an employee have to answer a customer asking if he/she is the owner?

I get asked this all the time, "Are you the owner?" The question is often made randomly while I am explaining a product or service. I find it very irritating but I try to answer with a polite, "No sir/no ma'm." However, there are some customers that don't drop the question. Is... show more I get asked this all the time, "Are you the owner?" The question is often made randomly while I am explaining a product or service. I find it very irritating but I try to answer with a polite, "No sir/no ma'm."

However, there are some customers that don't drop the question. Is this harassment? If it's clear they are not going to purchase anything, do I have to answer them? What's even worse and that it makes me a little paranoid is that I've had phone calls only asking me who is the owner.

This happened again yesterday. The customer just came in and asked what type of sales we did. He didn't ask about our products at all. Then he quickly switched topics and asked my co-worker if she was the owner. I stepped in and told him that we were closed and that he had to leave. Though he was rather rude to my co-worker, I feel so guilty for telling the customer to leave and for refusing to answer the question.
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