Exodus 9:16 - Why did God harden Pharaoh's heart?

[Exodus 9:16 ESV] But for this purpose I have raised you up, to show you my power, so that my name may be proclaimed in all the earth.

Paul quoted the verse in Roman 9.

[Romans 9:17-18 ESV] For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” So then he has mercy on whomever he wills, and he hardens whomever he wills.

It was God who hardened Pharaoh's heart. God raised up Pharaoh so that God's name might be proclaimed in all the earth.

[Exodus 11:9-10 ESV] Then the LORD said to Moses, “Pharaoh will not listen to you, that my wonders may be multiplied in the land of Egypt.” Moses and Aaron did all these wonders before Pharaoh, and the LORD hardened Pharaoh’s heart, and he did not let the people of Israel go out of his land.