In the correctly worked addition problem shown, where the

Hi, here are my two cents for this question

AB+BA = AAC

this means that B+A = X ( Say )

Now if we add any two digits the carry forward to tens digit can be either 0 or 1

If there was no carryforward from addition then X =C, if there was carry forward from addition then X=1C

Because in tens digit of addition A+B = AA, this means that carry forward from ones place was 1. if there was no carry forward from ones place then tens place would also be C .

this means in units digit the addition of B+A leads us to 1C, where C is in the units place of sum and 1 is taken as carry forward from addition.


So A+B= X= which is two digit number starting with 1_

so we know from ones place addition that B+A = 1C

so in tens place of addition we have A+B+1=AA

1C+1= AA
so 1C+1= 10A+A
1C+1= 11A
1C= 11A-1
1C= 11A-1
For any other value of A except 1 the value of C wouldn't have ten's place as 1. eg A= 2, C= 21, A=3 C=32
So A=1 now that means 1C=10
hence C =0

Now if A=1 , we have B= 9

AB+BA=
In Ones place we have B+A= 1+9=10, so 0 remains in units place of addition and 1 goes as carry forward.

In Tens place of addition we have A+B+1= 1+9+1= 11