9.
\( \;\;\begin{array} \hline \;\;\;2 & A &B\\ + A & B&1\\ \hline \;\;B&1 & 8\\ \hline \end{array} \)

We have condition as:

B+1=8.So, we got B=7

Also we have A+B=1

\(\Rightarrow\) A+7=11

A must be 4 to get unit's digit of A+7 as 1.So, A=4

And the last condition we have 2+A+1(carry)=B

Checking the values of A and B if it satisfies or not:

We have A=4 and B=7.Substituting, we have:

LHS: 2+A+1=2+4+1=7

RHS: B=7

Hence the values are verified.So we have A=4 and B=7