**The value of A is 7.**

*Strategy: Start with the units column.*From the units column, B + A = 2 or 12. If B + A = 2, then A is at most 2 and the final sum could not have three digits. Thus, B + A = 12.

From the tens column, A + A + a "carry" of 1 is an odd number, so B must be odd.

*Strategy: Start with the tens column.*In the tens column, A + A is at least 10, so A is at least 5. Test (A,B) for (5,7), (7,5), (8,4), and (9,3). A represents 7 and B represents 5.