Test: starting the investigation: how to identify elements, compounds, and mixtures

Elements, compounds and mixtures can be grouped into pure substances and impure substances.
Both elements and compounds is in the group of pure substances, while mixture is impure substance.

First talk about mixture, that would be easier. Mixture can be identified from many aspects.
First, in mixtures, the constitution elements still retain their own properties. For example in Iron and Sulphur mixture, iron can be attracted to magnets meanwhile iron II sulphide compund doesn't.
Mixtures can be separated by using simple physical methods, such as evaporation, filtration, chromatography etc.

In compunds, however we can only separate them using chemical methods, which include using electricity (electrolysis) or apply heat.
For example we know that water is a compund because we can separate it into hydrogen and oxygen by using electrolysis.

In elements, it's impossible to further simplify it, not even with chemical methods. For example, there's no way to further separate hydrogen into other elements.

Are there any options?