Why does Bitcoin send the "change" to a different address?
Two reasons:


So whoever sent to your "A" address can't claim to have sent you 31 bitcoins ("See!  Look on block explorer, there are two transactions sending to "A", one for 20 bitcoins and one for 11-- send me back the extra 11!")
Using a new change address makes it more difficult for other people to track of how many bitcoins you have or where you're spending them.