Question

Let F be a field, and suppose a EF, a *0. Prove that a has a unique multiplicative inverse.

Answer 1

Answer with Step-by-step explanation:

Let F be a field .Suppose $a\in F$ and $a\neq 0$

We have to prove that a has unique multiplicative inverse.

Suppose a has two inverses b and c

Then, $ac=1,ab=1$ where 1 =Multiplicative identity

$ac=ab$

$c=b$ (cancel a on both sides)

Hence, a has unique multiplicative inverse.