How do you prove the commutative property of multiplication for 4+ factors?

1. hamsa0

11
I don't know how to construct formal proofs but there is the obvious geometric approach for 2 and 3 factors. However, how do you prove the commutative property holds up for 4+ factors? You end up with a lot of different orders in which you can multiply the factors and you can't just construct a geometric object from them.

Last edited: May 23, 2011

Staff: Mentor

I don't see where geometry comes into it.
The commutative property of multiplication says that ab = ba. For 3 factors it would be abc = cba. For four factors, I guess you're trying to prove that abcd = dcba.
abcd = (ba)(dc) = (dc)(ba) = dcba

3. hamsa0

11
Ya after I posted this and hopped on the bus I realized it was a retarded question lol. Thanks for the response though man.