Step 1 (Dehydrohalogenation, alcoholic KOH, heat):
\[
\mathrm{CH_3{-}CHBr{-}CH_3 \xrightarrow[\ \Delta\ ]{KOH(alc)} CH_3{-}CH{=}CH_2\ +\ KBr\ +\ H_2O}
\]
Thus, \(\boxed{A=\mathrm{CH_3{-}CH{=}CH_2}\ (\text{propene})}\).
Step 2 (Anti-Markovnikov addition of HBr in presence of peroxides):
\[
\mathrm{CH_3{-}CH{=}CH_2 \xrightarrow[\ \mathrm{ROOR}\ ]{HBr} CH_3{-}CH_2{-}CH_2Br}
\]
Thus, \(\boxed{B=\mathrm{CH_3{-}CH_2{-}CH_2Br}\ (\text{1-bromopropane})}\).