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Allushta [10]
3 years ago
14

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

Mathematics
1 answer:
bezimeni [28]3 years ago
6 0

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.

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