God's Purpose in Pharaoh's Hardening

Exodus 11:9-10

And he went out from Pharao exceeding angry. But the Lord said to Moses: Pharao will not hear you, that many signs may be done in the land of Egypt.

And Moses and Aaron did all the wonders that are written, before Pharao. And the Lord hardened Pharao's heart, neither did he let the children of Israel go out of his land.