Which of the following properties is a measure of a material's resistance to deformation?

Hardness is indeed a measure of a material's resistance to deformation, particularly when it comes to permanent changes in shape or indentations. When a hard material is subjected to stress or a load, it is less likely to deform or show significant wear under pressure compared to softer materials. This property is crucial in applications where materials must withstand abrasive forces or maintain their structural integrity under mechanical stress.

While toughness relates to a material's ability to absorb energy and deform plastically without fracturing, it does not directly measure resistance to deformation itself. Elasticity refers to a material's ability to return to its original shape after being deformed, which involves reversible changes rather than complete resistance to deformation. Viscosity is a measure of a fluid's resistance to flow and deformation over time, which is pertinent to fluids but not a solid material's resistance to shape change. Thus, hardness is specifically focused on a material's ability to withstand deformation, making it the appropriate choice.