It is known that if k is a field and F: k[Xx,... , Xn] -» k[Xx, ... , Xn] is a polynomial automorphism, then deg(F_1) < (degF)"-1 . We extend this result to the case where k is a reduced ring. Furthermore, if k is not a reduced ring, we show that for any integer n > 1 and any integer X > 0 there exists a polynomial automorphism F such that deg(F-1) = A+(degF)"-'.