The word 'each' shows a single person/object or a group of people/things as a single unit.
When we use 'each', we refer to someone or something ONE AT A TIME.
So, the word each always take an inflected verb form -s (takes, bakes) and the words is, has, and was.
"Each other's peace" refers to Tom's peace and Jerry's peace ONE AT A TIME.
Well, just remember that the word 'each' simply signals the next word to be in singular form. That's just the rule.