$A$ on heating isomerizes to $B$. What is the structure of $B$?

Ethyl alcohol can be used in the preparation of which of the following?

The given reaction is known as :

The product $(A)$ of the reaction is:

Cyclohexanol is a

When a Grignard reagent reacts with $(B)$,product $(D)$ is obtained. Reactant $(A)$ of the above reaction is:
$(A)$ $\xrightarrow{PBr_3} (C)$ $\xrightarrow{Mg, \text{ether}} \text{Grignard reagent}$
$(A) \xrightarrow{Na_2Cr_2O_7, H_2SO_4} (B)$
$\text{Grignard reagent} + (B) \to (D) \xrightarrow{H_3O^\oplus} (3,4-\text{dimethylhexan-3-ol})$