Question

How does odysseus convince penelope he is odysseus?

Answer 1

Penelope, still not quite sure that the begger was indeed her husband, tested him. She ordered her maid to make up Odysseus' bed and move it from their bedchamber into hall outside his room. Odysseus was initially furious when he heard this because one of the bed posts was made from a living olive tree - he himself had designed it this way, and thus it could not be moved unless done by a god; he told her this, and since only Odysseus and Penelope knew this, Penelope accepted that he was her husband. She came running to him, hoping that he would forgive her. He forgave her, because he could understand why she had tested him and because he had passed the test.

Answer 2

When Odysseus finally arrives, Penelope is not convinced that it is him since she was visited by many impostors. At some point she asks one of the servants to move his bed and that's how he becomes mad and says that the bed cannot be moved unless you're a god because it was carved in living tree, something that only him and Penelope know. That's how he proves he's the real Odysseus.