Pyrometallurgy, Electrometallurgy, and Hydrometallurgy are three different processes used in metallurgy to extract metals from their ores. Each process is suitable for different types of ores and metals. The correct matches are:

- Pyrometallurgy = Fe, Zn, and Cu
- Electrometallurgy = Al, Mg, and Na
- Hydrometallurgy = Ag and Au

Now let's discuss each process in detail:

1. Pyrometallurgy:
Pyrometallurgy is a high-temperature process used to extract metals from their ores. It involves heating the ore in a furnace to produce a metal-rich product. This process is suitable for ores that can be easily heated and have high melting points. The correct matches for pyrometallurgy are:
- Fe (iron): Iron is commonly extracted from its ore, hematite, using pyrometallurgical processes such as blast furnace smelting.
- Zn (zinc): Zinc is extracted from its ore, zinc blende, through roasting and smelting processes.
- Cu (copper): Copper is extracted from its sulfide ores, such as chalcopyrite, through roasting and smelting processes.

2. Electrometallurgy:
Electrometallurgy involves the use of electricity to extract metals from their ores. It uses electrolysis, where an electric current is passed through an electrolyte solution containing metal ions to deposit the metal on the cathode. The correct matches for electrometallurgy are:
- Al (aluminum): Aluminum is extracted from its ore, bauxite, using the Hall-Héroult process, which involves electrolysis of molten aluminum oxide.
- Mg (magnesium): Magnesium is extracted from its ore, magnesite, through electrolysis of molten magnesium chloride.
- Na (sodium): Sodium is extracted through the electrolysis of molten sodium chloride.

3. Hydrometallurgy:
Hydrometallurgy uses aqueous solutions to extract metals from their ores. It involves dissolving the metal compounds in a suitable solvent, followed by precipitation or electrolysis to obtain the metal. The correct matches for hydrometallurgy are:
- Ag (silver): Silver can be extracted from its ore, argentite, through a cyanide leaching process, followed by precipitation of silver ions with a reducing agent.
- Au (gold): Gold can be extracted from its ore, gold-bearing quartz, through a cyanide leaching process, followed by precipitation of gold ions with a reducing agent.

In conclusion, the correct matches for the given options are A, B, and C. Pyrometallurgy is suitable for Fe, Zn, and Cu extraction, Electrometallurgy is suitable for Al, Mg, and Na extraction, and Hydrometallurgy is suitable for Ag and Au extraction.