A cloak of invisibility provides MC2 and invisibility. Its appearance is chosen at random each game, and (if you're not already invisible) auto-identifies when worn.

Note that if you eat an invisible stalker corpse while invisible from another source, you gain permanent invisibility. Also keep in mind that shop keepers will not let you enter their shops if you are invisible, so you will need to remove your cloak to enter a shop. If you have invisibility from another source, see invisibility.