Question

Determine all elements of an integral domain that are their own inverses under multiplication

Answer 1

A ringRis a set with two binary operations, addition and multiplication, satisfying several properties:Ris an Abelian group under addition, and the multiplication operation satisfies the associative lawand distributive lawsandfor everyThe identity of the addition operation is denoted 0. If the multiplication operation has an identity, it is called a unity. If multiplication is commutative, we say thatRis commutative.LetRbe a commutative ring andabe a nonzero element ofR. If there exists a nonzerosuch thatwe say thatais a zero-divisor.IfRhas a unity and has no zero-divisors, we say thatRis an integral domain.