Isotropic Material:
An isotropic material is one that exhibits the same physical properties in all directions. These properties include mechanical, thermal, and electromagnetic characteristics.

Elastic Properties:
Elastic properties refer to the ability of a material to deform under stress and return to its original shape when the stress is removed. These properties are important in determining a material's response to mechanical forces, such as stretching or compression.

Elastic Properties in All Directions:
In the context of this question, the term "elastic properties in all directions" means that the material's response to stress is the same regardless of the direction in which the stress is applied. This means that the material will exhibit the same amount of deformation and strain in all directions.

Answer Explanation:
The correct answer is option 'A', isotropic. An isotropic material is one that has the same elastic properties in all directions. This means that when stress is applied to an isotropic material, it will deform and exhibit strain uniformly in all directions.

Other Options:
- Homogeneous: Homogeneous refers to a material that has the same composition and properties throughout its structure. While a homogeneous material can be isotropic, it is not necessarily the same thing. A material can be homogeneous but anisotropic, meaning it has different properties in different directions.
- Homogeneous Isotropic: This option combines the concepts of homogeneity and isotropy. It is not the correct answer because it is redundant, as isotropy already implies homogeneity.
- Rigid: Rigid materials do not deform under stress and have zero strain. This is the opposite of an elastic material and is not the correct answer.

In summary, the material which has the same elastic properties in all directions is called an isotropic material. This means that the material will deform and exhibit strain uniformly in all directions when stress is applied.