Read the excerpt from The Odyssey. At this he gave a mighty sob and rumbled:
'Now comes the weird upon me, spoken of old.
A wizard, grand and wondrous, lived here—Telemus,
a son of Euryinus; great length of days
he had in wizardry among the Cyclopes,
and these things he foretold for time to come:
my great eye lost, and at Odysseus' hands.
Always I had in mind some giant, armed
in giant force, would come against me here.
But this, but you—small, pitiful and twiggy—
you put me down with wine, you blinded me.
Come back, Odysseus, and I'll treat you well,
praying the god of earthquake to befriend you—
his son I am, for he by his avowal
fathered me, and if he will, he may
heal me of this black wound—he and no other
of all the happy gods or mortal men.’

Why does the Cyclops invite Odysseus back to the island?

He realizes that Odysseus was destined to take his eye.
He wants to obey the Greek custom of providing food and shelter to guests.
He fears far more harm will come to him if does not befriend Odysseus.
He wants to take revenge on Odysseus.