I hope I dint make a mistake here
AB- Tens digit A UNITS DIGIT B cane be represented as 10a+b
BA - SIMILARLY 10b+a
10a+b+10b+a = aac
11a+11b = aac
11(a+b) = aac (aac is a multiple of 11)
The only three digit multiple of 11 with the hundreds and tens digit the same is 110,220,330 etc withe C being 0 but since u are adding two 2 digit numbers aac can be at the max 198 and hence 110 fits the bill
Hence C must be 0.