1. The problem statement, all variables and given/known data Let R be an Integral Domain. Prove that if a,b are elements of R and both a and b are units in R, then prove a*b is a unit of R. 2. Relevant equations a is a unit in R if and only if there exists an element u in R such that au=1=ua where 1 is the identity element of R. We also know that since R is an integral domain, that R is a commutative ring with identity. Since R is a ring, R is closed under multiplication therefore a*b would still be an element of R. 3. The attempt at a solution Given that both a and b are elements of R, and both a and b are units. Then by the definition of a unit there exists s,t that are elements of R such that a*s=1=s*a and b*t=1=t*b. Somehow I need to multiply a and b together. So, Let a*b be a unit in R, then there exists w that is an element of R such that: w(a*b)=1=(a*b)w. I'm lost from this point forward... any help?