Right answer is (b) identity property
The best explanation: For identity e, a+e=e+a=e, a*e = a+e+ae = a => e=0 and e+a = e+a+ea = a => e=0. So e=0 will be identity, for e to be identity, a*e = a ⇒ a+e+ae = a ⇒ e+ae = 0 and e(1+a) = 0 which gives e=0 or a=-1. So, when a = -1, no identity element exist as e can be any value in that case.