Is my piano student flirting with me, and how should I handle it?

So I've been teaching a guy for a while. He's 21 I'm 25. I was showing him a scale but instead of looking he just stared at my reflection in the piano and was smiling!!

He also stayed for a whole hour and the lessons are only thirty minutes.

The problem is I like him too and I don't know what to do because it's killing me. I have to stay professional. He always stays overtime but lately he's been asking and saying it's up to you?

I guess he's just being respectful of my time. He's really sweet and I can't help but have some feelings for him

Is my piano student flirting with me, and how should I handle it?
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