I haven't read the responses, but the correct answer is to switch cells. Staying in the orginal cell gives Prisoner A a 1/3 chance of being pardoned while switching gives him a 2/3 chance of being pardoned.
This puzzle is a variation of the Monty Hall Problem. It's a counter-intuitive problem. Personally, I've always had problems wrapping my head around it, but the math is clear IMO. For those who would like to explore the issue further, just Google:
Monty Hall Problem
Monty Hall Problem explained.
And this site gives a decent explanation as to why switching is the best option
Monty Hall Problem Explained With Worked Solutions