using "呢" without making the sentence a question?

I was talking to my Chinese friend and she said "吃了呢～" is a cute way of replying to the greeting "你吃了吗？". I assumed "吃了呢～" meant "have you eaten?" but she said it meant "I have eaten".

It really confused me and she couldn't explain why it wouldn't be a question, can anyone else me understand and give me other examples? I'm very much a beginner in Chinese, so is this an advanced usage of "呢"?

submitted by /u/halogem
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