Which should be the most basic feature in determining whether a thing is living or not: genetic material or cellular structure?

This question is hard to answer because it depends on how you decide to define a living thing, what cellular structures you are looking for, what you mean with genetic material, and what you mean with "basic feature".

 

In my opinion, the answer to this question will change depending on who asks it. For example, if your professor is of the opinion that Viruses are not alive and you just went over viral genetics, then she might be looking for the answer "Cellular structure because viruses also contain genetic information and are not alive". However, perhaps your professor chose to define life as any entity that carries genetic information, and also talked about the formation of vesicles that might look like microorganisms under the microscope. In this case, he might be looking for "genetic information".

 

It's a question which can be interpreted in many different ways, and so there is no "correct" answer.

Which should be the most basic feature in determining whether a thing is living or not: genetic material or cellular structure?

 

A living thing has both genetics and cellular structure and same to nonliving things, FYI even a paper has cellular structure we call cellulose.

 

Maybe the question will be on how their genetics and cellular structure works because almost all living things has capability to multiply simply because if it does not multiply it won't survive.