Which state(s) of matter possess negligible compressibility and rigid in nature?

Solid

The correct answer is option 2. Solid.

Solids have a definite shape, distinct boundaries and fixed volumes, that is, have negligible compressibility.

Solids have a tendency to maintain their shape when subjected to outside force.

Solids may break under force, but it is difficult to change their shape, so they are rigid.