I need to prove the following:
a) Addition on Q is communitive.
b) Multiplication on Q is associative.
c) Multiplication on Q is communitive.
I figured out how to prove addition on Q is associative.. Here is what I did:
([a,b] + [c,d]) + [e,f]
= [ad + bc, bd] + [e,f] = [(ad+bc)f + (bd)e, (bd)f]
= [adf+bcf+bde, bdf] = [a(df) + b(cf+de), b(df)]
= [a,b] + [cf + de, df] = [a,b] + ([c,d] + [e,f])
I can't figure the others out. any help would be appreciated.