If you have to show this "the long way", then just do the multiplications, and see what you get. It's long and boring, but pretty straightforward.
^^ That's the one...can someone please help me prove it? I'm not allowed to use the "a1(b2*c3-b3*c2)..." formula. I have to use the silly row-column subtraction/addition arithmetic method, where you have to write r1'=r1-r2, c3'=c3-c2, stuff like that after every relevant step...