Malleability is the important mechanical property for a material to be forged or rolled into thin sheets successfully.

Explanation:
Malleability is the ability of a material to undergo plastic deformation under compression, without cracking or breaking, and to be rolled or hammered into thin sheets. It is a critical property for materials used in forging and rolling processes.

Malleability is a result of the arrangement of atoms or molecules in a material. In malleable materials, the atoms or molecules can easily slide past each other when a force is applied, allowing the material to be shaped without fracture. This property is particularly important in processes like forging and rolling, where the material is subjected to high compressive forces.

When a material is forged, it is heated and then shaped by applying compressive forces. The material needs to be malleable so that it can be easily deformed and shaped without cracking or breaking. If the material is brittle, it will fracture under the applied forces, making it unsuitable for forging.

Similarly, in the rolling process, the material is passed through a series of rollers to reduce its thickness and increase its length. Malleability is essential for this process as well since the material needs to be able to deform and flow under the pressure of the rollers without tearing or breaking.

In contrast, other mechanical properties mentioned in the options have different implications in the context of forging and rolling:

- Brittleness refers to the tendency of a material to fracture or break when subjected to stress. Brittle materials are not suitable for forging or rolling as they cannot withstand the compressive forces involved without cracking.

- Ductility refers to the ability of a material to undergo plastic deformation under tension. While ductility is important in other processes like wire drawing, it is not the primary property needed for successful forging or rolling.

- Elasticity refers to the ability of a material to deform under stress and return to its original shape when the stress is removed. Elasticity is not the most important property for forging or rolling, as these processes involve permanent deformation of the material.

Overall, malleability is the crucial mechanical property for a material to be successfully forged or rolled into thin sheets, as it allows the material to undergo plastic deformation without fracture or breakage.