An element x in R is called nilpotent if x = 0 for some m € 2¹. Let x be a nilpotent element of the commutative ring R (a) Prove that x is either zero or a zero divisor. (b) Prove that rx is nilpotent for all r € R. (c) Prove that 1 + x is a unit in R. (d) Deduce that the sum of a nilpotent element and a unit is a unit.

please provide some explanation with the taken steps in the attached exercise, Im quite new to abstract algebra