Please answer all parts

6. Let R be a ring with identity 1. Define a new operation on R by nobmath- ab for all a, be R. (a) Show that the operation o is associative. (b) Show that there is an element e E R such that noczeoama for allaER. (Hint: first try writing out the "multiplication table" for the o operation in a small ring like Za.) (c) Show that there is an element = E R such that for all a E R. (d) Show that for all a E R, aoa = a if and only if a? = a in R. (e) Deduce that if R is an integral domain, the only solutions to the equation non = 0 area = 0 and a = 1