Vitamin A is an essential nutrient for various cell reactions. It is also an antioxidant, which means that it fights oxygen free radicals, which damage DNA, leading to cancer.
One article (1) looked at vitamin A and its prevention of cancer. They noted that, by being an antioxidant, Vitamin A is able to prevent cancer caused by exposure to environmental toxins and ionizing radiation. They also noted that, by being an antioxidant, vitamin A is believed to prevent cancer when taken internally.
Animal studies in the laboratory who had increased amounts of antioxidants like vitamin A had a decreased risk for cancer. This type of study has not been done on humans so it can’t be said for sure that vitamin A can prevent cancer in a human population.
Source: 1.Antioxidants and cancer prevention. http://www.cancer.gov/about-cancer/causes-prevention/risk/diet/antioxidants-fact-sheet. Accessed 9/12/16.