Since the units place contains a 6, BxB should give a number with 6 in units place. That is possible when B = 4 or 6.

If B = 4, (10A + B)x(B) = 96 becomes (10A + 4)x4 = 96

40A + 16 = 96, gives A = 2.

If B = 6, (10A + B)x(B) = 96 becomes (10A + 6)x6 = 96

60A + 36 = 96, gives A = 1.

Therefore, A = 2 B = 4 or A = 1 B = 6 (Both are valid)