The correct answer is: A. Carbon
Carbon is the only non-metal that shows allotropy in the liquid state. Allotropy is the property of some chemical elements to exist in two or more different forms, or allotropes, with different physical properties. Carbon has two common allotropes in the liquid state: diamond and graphite. Diamond is a hard, transparent solid with a cubic crystal structure. Graphite is a soft, black solid with a layered crystal structure.
Sulphur, phosphorus, and bromine are all non-metals that do not show allotropy in the liquid state. Sulphur exists in two common allotropes: rhombic sulphur and monoclinic sulphur. Rhombic sulphur is a yellow, crystalline solid with a rhombic crystal structure. Monoclinic sulphur is a yellow, crystalline solid with a monoclinic crystal structure. Phosphorus exists in four common allotropes: white phosphorus, red phosphorus, black phosphorus, and violet phosphorus. White phosphorus is a waxy, white solid that is highly flammable. Red phosphorus is a red, amorphous solid that is less flammable than white phosphorus. Black phosphorus is a black, crystalline solid that is very stable. Bromine is a red-brown, liquid non-metal that is highly corrosive.
In conclusion, the only non-metal that shows allotropy in the liquid state is carbon.