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In order to answer your question, we need to turn it around and look at the chemistry of living things, and then say that things that don't match that definition are non-living.
Living things, on Earth at least, are based on just a few elements, carbon being the most important. Because each carbon atom can form four covalent (sharing) bonds, carbon is able to create complex molecules. Theses molecules always have some hydrogen atoms in them as well, and usually there's oxygen in them too. Those are the "big three", the commonest life molecules. Then there are nitrogen, calcium, phosphorus, chlorine, potassium, sulfur, sodium, and magnesium; this list is in descending order of amount found in the human body.
Non-living things can be composed of any combination of elements, but will always lack the carbon-hydrogen-oxygen main structure.
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