Prove that exp[A].exp = exp[A+B] only if A and B commute. 1. The problem statement, all variables and given/known data Prove that eA.eB = e(A+B) only if A and B commute. The attempt at a solution I expanded both sides of the equation. (1+A+A2/2!...)(1+B+B2/2!+..) = (1+(A+B)+(A+B)2/2!+..) Now how to proceed ?