Answer :

while multiplying 6 and B we get a number whose one's digit is B again

It is only possible when B = 0, 2, 4, 6, or 8


If B = 0, then the product will be 0.


Therefore, this value of B is immposible.


In that case,


If B = 2, then B × 6 = 12 and 1 will be a carry for the next step


6A + 1 = BB = 22


6A = 21


Hence, any integer value of A is not possible


If B = 6, then B × 6 = 36 and 3 will be a carry for the next step


6A + 3 = BB = 66


6A = 63


Hence, any integer value of A is not possible


If B = 8, then B × 6 = 48 and 4 will be a carry for the next step.


6A + 4 = BB = 88


6A = 84


Therefore,


A = 14


However, A is a single digit number. Therefore, this value of A is not possible


If B = 4, then B × 6 = 24 and 2 will be a carry for the next step.


6A + 2 = BB = 44


6A = 42


And hence, A = 7


The multiplication is as follows:



Hence, the values of A and B are 7 and 4 respectively


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