In book 22, who is the first suitor to die?
Appropriately enough, it is the loathsome Antinous who's first to get his comeuppance—and a richly deserved comeuppance at that. Antinous is the unofficial leader of Penelope's suitors, eating Odysseus out of house and home while they pester his wife for her hand in marriage. Antinous is by far the most arrogant and disrespectful of all the suitors. Not only does he disrespect Odysseus by courting his wife, he also plans to murder Telemachus upon his return to Ithaca. Worse still, he throws a stool at Odysseus when he returns to the palace disguised as a beggar.
One thing we must always bear in mind is that Odysseus is a king, and this is his palace. It's not possible for anyone to have behaved as disrespectfully towards Odysseus as Antinous has done. By the standards of the time, and not just in ancient Greece, he has committed the very highest of high treason. As such, when his inevitable end finally comes, it is more than simply poetic justice that is meted out by Odysseus's arrow.
In Book XXII, Odysseus, who had previously posed as a beggar, reveals his true self by using his bow, which only he is strong enough to use, to kill Antinous. The other suitors are still unaware that the man in front of them is Odysseus, and they reproach him for killing a man whom they describe as the "foremost youth in Ithaca." Odysseus mocks them, and despite their attempts to suggest that Antinous was actually behind the whole plot to win the hand of Penelope, he tells him that he will kill them all. With the help of Athena and his son, Telemachus (who Antinous had plotted to murder), he slaughters every single one of them except for two men whom Telemachus intervenes to save. He also kills twelve of the maidservants who had slept with the suitors and the goat herder who tried to help them. This brutal and horrific bloodletting began with the death of Antinous.