Question

difference of additive inverse of x and the multiplicative inverse of y is​

Answer 1

Hi there.

: itz Arpan here. ✌✌

your answer is -_-

So we have an element a in R which is a ring with 1 .

This includes having 2 binary operators +,∗ and we call them addition and multiplication.

The mentioned 1 is the neutral element for multiplication. 0 is the one for addition.

This means: ∀r∈R

1∗r=r∗1=r

0+r=r+0=r

So going back to our a , an element g is called additive inverse if and only if

a+g=g+a=0

Same story for the multiplicative inverse of a

a∗h=h∗a=1

So they’re similar in that regard.

But in general h≠g

So a∗g≠1

and a+h≠0

So that’s the difference.