In The Odyssey, how does Odysseus apply what he learns from Agamemnon in the underworld to his own situation in Ithaca?

It is in Book Eleven of this epic classic that Odysseus
makes his voyage down into the underworld and meets with various characters. Agamemnon
tells his former comrade how he met his end at the hands of his wife, Clytemnestra, and
he expresses envy at Penelope's faithfulness compared to the treachery of his own
deceitful wife.

We can perhaps see in this comparison that
Agamemnon draws between his wife and Penelope the seeds of doubt that cause Odysseus to
spend so long trying to ascertain Penelope's faithfulness when he reaches Ithaca. He
could have overthrown the suitors much more quickly, but having been given this
information, he becomes suspicious of his wife, not wishing to share the same fate as
Agamemnon.