Q = PAPT
= PT(Q2016)P
= PT * PAPT * PAPT * PAPT * .......... * PAPT * P
now |PT * P| = 1
so all PT * P will become 1
ultimately we will get final value as A2016
now,
Value of |A| = 1*1 - 0*1 = 1
so |A2016| = 12016 = 1
Only first option is matching, so answer should be option 1
You can also solve by finding A2 then A3 and obtain the pattern to get A2016