Chromatography can show whether a substance is pure. A pure substance contains only one compound, so it gives a single spot on a paper or TLC chromatogram. An impure substance is a mixture, so it gives two or more spots. The test is repeated with a second solvent, because two different substances can have the same Rf value in one solvent but not in another.
To identify the dyes in an unknown ink, a spot of the ink is placed on the baseline next to spots of known inks. After the run, compare the positions of the spots and their Rf values. If a spot from the unknown ink lines up with a known one, they are probably the same dye. TLC is often used when only a tiny amount of sample is available and a clearer, faster separation is needed.
Gas chromatography is used for mixtures that can be turned into a vapour. A carrier gas moves the vaporised mixture through a column. Each substance leaves the column at a different time and gives a separate peak on the output. Three peaks means at least three substances, and a pure substance gives one peak.