What if the 1st person is left handed and he is B?
for the 1st question, he can not raise his right hand because he is not A, neither to raise his left hand which means (yes),and that is not true.
There is no contradiction here. If first person is left handed and he is B, he has to answer the question 'will I raise my right hand for the question "are you A?"?'. Answer is 'Yes, right hand will be raised if the question was "Are you A"'.. Since B is left handed, he will finally raise his left hand to signify "Yes".
I think my approach is essentially the same.
nice trial... but take it in an easier way..