A mufflers only real purpose is to make your car less noisy and is a legal requirement, cars actually preform better when the airflow is more free (ie without a muffler) it would be hard to install a muffler upside down/backwards, and it would just not work as effectively (there would be no point)
Muffler or Silencer as we call it in India, is connected to the exhaust of the engine to reduce noise of the engine. It does so by destructive interference in sound waves similar to destructive interference in light. One back draw of silencer is back pressure to the engine which reduces its efficiency.