Let f be a field, and suppose a ef, a *0. prove that a has a unique multiplicative inverse.

Answer with Step-by-step explanation:

Let F be a field .Suppose and

We have to prove that a has unique multiplicative inverse.

Suppose a has two inverses b and c

Then, where 1 =Multiplicative identity

(cancel a on both sides)

Hence, a has unique multiplicative inverse.

b) well because you get well