If someone doesn't respond back to your greeting like "Hello" or "Good Morning" do you say anything back?

I'm curious to see what others thought are upon this.

I have a co-worker who doesn't respond back to my Good Mornings, I just continue to do it daily to her, maybe some day she will respond back.

I was thinking of asking her some time "Have you ever felt awkward when someone doesn't respond back to your greeting?" with a smile on my face to see what she would say.

I don't take it personally that I don't get a response because I know that is just her. She doesn't talk much in the first place and normally just complains if she does talk. Though if I ask her that question in a positive tone with a smile maybe she will see how it makes you feel more positive when you respond back to others.