The correct options for the amphoteric nature of aluminum employed in the extraction of aluminum are Baeyer's process and Hall's process.

1. Baeyer's process:
- In Baeyer's process, aluminum is extracted from its ore, bauxite.
- Bauxite is first purified to remove impurities and is then converted into aluminum hydroxide by dissolving it in sodium hydroxide solution.
- The aluminum hydroxide is then heated to obtain alumina (Al2O3).
- Alumina is an amphoteric compound, meaning it can react with both acids and bases.
- In Baeyer's process, alumina reacts with a strong base, such as sodium hydroxide, to form sodium aluminate, which is soluble in water.
- The impurities present in alumina, such as iron oxide and silica, remain insoluble and are separated.
- The soluble sodium aluminate is then treated with carbon dioxide gas to precipitate aluminum hydroxide.
- The aluminum hydroxide is then heated to obtain pure aluminum oxide, which is used for the extraction of aluminum by electrolysis in Hall's process.

2. Hall's process:
- Hall's process is the primary method used for the extraction of aluminum.
- It involves the electrolysis of pure aluminum oxide (obtained from Baeyer's process) dissolved in molten cryolite (Na3AlF6) at high temperatures (around 950°C).
- Cryolite lowers the melting point of the alumina and increases its conductivity.
- Aluminum oxide is dissolved in the molten cryolite, and a direct current is passed through the electrolytic cell.
- The aluminum oxide is reduced at the cathode, forming molten aluminum metal, which collects at the bottom of the cell.
- At the anode, oxygen gas is evolved.
- The molten aluminum is periodically tapped off from the cell and further processed to obtain the desired aluminum products.

In conclusion, both Baeyer's process and Hall's process utilize the amphoteric nature of aluminum to extract pure aluminum from its ore. Baeyer's process involves the conversion of bauxite into alumina, while Hall's process involves the electrolysis of pure aluminum oxide.

Baeyer's process and hall's process are used to remove Fe₂O₃ impurity from Bauxite.