Prove that if a and bare nonzero, then (ab)- = ab-. That is, the multiplicative inverse of ab is the element a-6-. Hint: Don't try to prove this by writing something like (ab)-1 = 1 ab 1 1 a b = 1 a a-6-, because when you write , you're actually applying the property you're trying to prove. Instead, see the proof of the statement -(a + b) = (-a) + (b) in my notes.