The Invisible Cat is actually, contrary to popular belief, a cat that is NOT invisible! He just thinks he is so he can escape danger which is a pretty good idea for a quick escape.
Many people fall for this trick but some, including Chuck Norris and Ender Wiggin, are smart enough to see that he is visible 24 hours a day. He thought he gained this special ability when Wal Didney told him to just believe in magic and anything is possible. The Invisible Cat (just called Cat back then) took this seriously and now believes he can become invisible at will. He is a minion of Happycat because he fell for Invisible Cat's trick.