this kind of question should be answered by "yes" or "no". In this case, we say "verb + 了" meaning "yes" and "没有" meaning "no". "吃“ is the verb here, so you can say: 吃了 or 没有. "没有" is just like english --- "have not". Have you eaten? -- "no, I haven't". If you want to say: not yet, in chinese it's "还没有" or "还没"