what do penelope action reveal about her character?

Are you referring to her refusing the suitors? She is pretty clever. Penelope retrieves Odysseus' great bow from the storeroom and her maids bear axe heads into the main hall. Penelope explains the game: whoever can string her husband's bow and shoot an arrow through the twelve axeheads will marry her. Telemachus gives it a try first; he is unable to string the bow three times. Other suitors fail to string the bow.