Haskell: downpair :: (Monad m) => m (a, b) -> (m a, m b) implementation

Question

I'm trying to implement function downpairs which takes monad of pairs and transform it into pair of monad

My current implementation is

import Control.Monad
import Control.Arrow
import Data.Maybe

downpair :: (Monad m) => m (a, b) -> (m a, m b)
downpair = ((return . fst =<<) &&& (return . snd =<<)) 

main = do
    print $ downpair $ Just ("Hello", "World")

Is there way to implement downpair in more compact maner?

PS Sorry for my poor English

Answer 1

(return . fst =<<) can be replaced by fmap fst. Your definition then becomes

downpair = fmap fst &&& fmap snd