Solid A is a very hard electrical insulator in solid as well as in molten state and melts at extremely high temperature. What type of solid is it?

The solid ‘A’ is a covalent solid, such as diamond. As it is an electrical insulator in both solid and molten form and melts at an extremely high temperature.

Explanation-In covalent solids the constituent particles (i.e. atoms) form a network of covalent bonds which make them very hard and also very high melting points.

Further they are electrical insulator in solid as well as in molten state because they do not contain any ion (like ionic solids) or free electrons (like metallic solids) in solid or in molten state.

(Note- For any compound to show electrical conductivity either free electrons or free ion must be available.)