Replace A, B, C by suitable numerals.
$A \times B=B \Rightarrow A=1$
In the question:
First digit = B+1
Thus, 1 will be carried from 1+B2 and becomes (B+1) (B2 -9) B.
∴ C = B2 -1
Now, all B, B+1 and B2 -9 are one digit number.
This condition is satisfied for B=3 or B=4.
For B< 3, B2 -9 will be negative.
For B>3, B2 -9 will become a two digit number.
For B=3 , C = 32 - 9 = 9-9 = 0
For B = 4, C = 42 -9 = 16-9 = 7
A=1, B=3, C = 0
A=1, B=4, C = 7