Suppose that R and S are rings with identity. Let (r, s) in R × S. Show that

(r, s) is unit in R × S <=> r is a unit in R and s is a unit in S.

Also, if (r, s) is a unit in R×S, show that inverse of (r, s) = (inverse of r, inverse of s)

(Hint: It is efficient to prove the last statement and the implication “<=” in the first statement at the

same time.)

um....can anyone help!!! urgent!!! Thanks very much :)