Thanks GMAT TIGER for responding. However, I am difficulty understanding it.
Statement 1 implies that either A = 0 "or" AB=1. From this how can we conclude that AB=1 is not possible?
Similarly Statement 2 implies that either B=0 "or" AB=1.
Therefore, Statement 1 and 2 will imply that AB=1. That is, I think answer should be (C).
But the answer in GMATCLUB Challenge is given as (E).
This is data sufficiency problem - since you have two options for AB (i.e 0 or 1) then you don't have sufficient data to answer the problem.
Assume A=0 B=0 then AB = 0 in option (C) !
the correct answer is (E)