Nicki Minaj and Mariah Carey — Already at Each Other’s Throats on ‘American Idol’

Mariah Carey wasted no time proving what we told you 2 weeks ago — there’s only room for one diva on “American Idol.”Carey and Nicki Minaj went at it during the first “A.I.” taping Sunday in NYC. When Nicki started critiquing a contestant, Mariah…