While adding A and 3 we obtain 6. There can be two cases.

(i) First step is not producing a carry

In that case,

A comes to be 3 as 3 + 3 = 6

Taking the first step in which the addition of B and 7 is giving A (i.e., 3), B should be a number such that the units digit of this addition comes to be 3.

It is only possible only when B = 6

In that case, A = 6 + 7 = 13

But, A is a single digit number

Hence, it is invalid.

(ii) First step is producing a carry

In that case,

A comes to be 2 as 1 + 2 + 3 = 6

Taking the first step in which the addition of B and 7 is giving A (i.e., 2), B should be a number such that the units digit of this addition comes to be 2.

But, it is possible only when B = 5 and 5 + 7 = 12

Hence, the values of A and B are 2 and 5 respectively