Odysseus proved his identity to his wife, Penelope, and son, Telemachus, by revealing a scar that he received during a hunting accident when he was young. The scar was not known to anyone else and was the proof they needed to confirm that Odysseus was indeed who he claimed to be. In addition to revealing the scar, Odysseus also shared details of their life that only the real Odysseus would know, this helped Penelope to finally believe and accept that he was her husband.