Statement - (A) : The difference between a new torch light cell and an old one is due to increase in internal resistance.
Statement - (B) : At 0 kelvin specific resistance of perfect insulator is infinity.

In a torch light cell, the internal resistance keeps increasing with usage due to decrease in concentration of the electrolyte. 

For a perfect insulator, specific resistance decreases with increase in temperature and vice versa. So at 0 k, it's specific resistance becomes infinity.