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

Let f be a field, and suppose a ef, a *0. prove

isabelperez063

04.01.2022

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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sawyerharper

07.05.2022

You are absolutely correct, second option is the correct answer.

Step-by-step explanation:

Diameter of vase = 6 inches

Therefore, radius r = 3 inches

Diameter of marbles = 3 inches

Radius of marbles = 1. 5 inches

Height of water h = 10 inches

Volume of water in the vase = Volume of vase - 8 times the volume of one marble

$= \pi r^2h - 8\times \frac{4}{3} \pi r^3 \\\\= \pi (3\: in) ^2(10\: in) - 8( \frac{4}{3} \pi (1.5\: in) ^3) \\\\$

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