Olive oil is packed with antioxidants called polyphenols which act to protect the oil from oxidation. The heat required to fry food cannot change the chemical composition of olive oil and therefore keeps all its nutrients intact.
When used under right temperatures with the proper cooking techniques olive oil forms a crust on the surface which inhibits the penetration of oil and improves its flavor. Food fried/cooked in olive oil has a lower fat content than food fried in other fats, and has substantially more nutrients, making olive oil more suitable for weight control.

Not only can you fry with extra virgin olive oil, but you should. It stands up well to heat due to its monounsaturated fatty acid and polyphenolic content; it’s also a safer, healthier, and tastier choice compared to other fats. High monounsaturated fat percentage helps olive oil stabilize better when exposed to high heat. Unlike olive oil, other types of oils that are high in polyunsaturated fats quickly oxidize at high heat and release harmful free radicals.