Here the same word sits in front of a noun and tells you who or what that noun belongs to: Inuit art, an Inuit village, Inuit words. The form never changes and it keeps the capital I. It does not take -er or -est, because it is not describing an amount of something; it is naming a connection.

Inuit is the name of a real group of people, so it is written with a capital I. The word came into English from the Inuit language itself, where it means "the people". In that language, one person is an Inuk, and two or more are Inuit. Everyday English also uses Inuit for one person, which is what this sense shows. For more than one, English usually keeps the same form: three Inuit. The spelling Inuits does exist, but it is rare and many writers avoid it.

With the in front, the word stops pointing at an individual and points at the group. It behaves as a plural, so the verb is plural too: the Inuit have, the Inuit live. There is no -s on the end. You will meet this form most often in writing about history, land, language and culture, where the topic is the group over a long time rather than any one person.