Show that it is undecidable if two Turing Machines accept the same language
Let's restrict ourselves to Turing machines that ignore their input. Now suppose you have two Turing machines:


Some given one T.
Another that loops forever.


If you could decide if they accept the same language, you'd be able to decide if T halts or not. This is impossible - see the halting problem.



This applies to SW/HW as well. It's undecidable if two programs perform the same computation or not.