The structure of ‘A’ and the type of isomerism with the final product
in the above reaction are respectively: 

1. Prop-1-en-2-ol and Metamerism
2. Prop-1-en-1-ol and Tautomerism
3. Prop-2-en-2-ol and Geometrical isomerism
4. Prop-1-en-2-ol and Tautomerism

Hint: Oxymercuration-Demercuration reaction

The chemical reaction is as follows:

[A] is prop-1-en-2-ol, which undergoes tautomerism to form acetone.