Question

In the following, find the digits represented by the letters:
$1A$
$\underset{–}{\times 1A}$
$\underset{–}{1BA}$

Answer 1

In the given problem, the multiplication of $A$ with $A$ itself gives a number whose ones digit is $A$ again. This happens only when $A=1,5,6$.

If $A=1$ then the multiplication will be $11\times 11=121$. However, here the tens digit is given as $B$, therefore, $A=1$ and $B=2$ are possible.

Hence, the letter $A=1$ and $B=2$.