To solve this question, we need to analyze the given reaction sequence and determine the types of mechanisms involved in forming the products A and B.
- The first step involves the formation of compound A using \(H_2O\) via an \(S_N1\) reaction. In \(S_N1\) reactions, the reaction proceeds through a carbocation intermediate which leads to the possibility of racemization. This is because the planar carbocation can be attacked from either side, resulting in the formation of a racemic mixture. Therefore, statement I is correct.
- The formation of compound B is described using \(NaOH\) through an \(S_N2\) mechanism. In \(S_N2\) reactions, the nucleophile attacks the carbon atom from the opposite side of the leaving group, resulting in inversion of configuration. This means that the original configuration is inverted to produce the product. Therefore, statement II is correct.
Based on the analysis, the correct choice is that both statements I and II are correct.