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
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Probus
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