Find the values of the letters in the following and give reasons for the steps involved.
$AB\underset{–}{\times 5}\underset{–}{CAB}$

As $B\times 5=B$, B has to be either $5$ or $0$.

If $B=0$, then A has to be 5 as $A\times 5=A$.

So, $A=5,B=0$ and $C=2.$

If $B=5$, then $A=2$ so that $A\times 5$ with carry over ends with $A$.

Hence, $A=2,B=5,C=1.$