In the context of the addition problem involving AB and BA, what is the sum of the resulting digits?

To understand why the sum of the digits resulting from the addition problem involving the numbers AB and BA can be two digits, let's first explore what AB and BA represent in this context.

AB signifies a two-digit number where A is the tens digit and B is the units digit. Therefore, it can be expressed as:

• AB = 10A + B

Similarly, BA signifies the number where B becomes the tens digit and A becomes the units digit:

• BA = 10B + A

Now, when we add AB and BA, we perform the following calculation:

(10A + B) + (10B + A)

This simplifies to:

10A + B + 10B + A = 11A + 11B = 11(A + B)

The sum of the digits, A + B, can vary depending on the values of A and B. The individual digits A and B can range from 0 to 9 (assuming it's a decimal system). Thus, A + B can take on values from 0 (if both A and B are 0) to 18 (if both A and B are 9).

When we multiply the sum by 11, we see that