Monopolies exist in many markets in real life for very different reasons:
Ownership of a Key Resource: When one company exerts sole control over a resource that is necessary for the production of a specific product, the market may become a monopoly. For example, the only medication deemed acceptable to treat a disease comes from a particular ingredient X, and knowledge of this ingredient X is owned by a single family owned company. The company can, therefore, be said to have a monopoly over ingredient X that is needed to cure the disease because it is the only company that can produce a product deemed acceptable.
Government Franchise: In certain instances, a monopoly may be explicitly created by the government if it grants a single company, whether private or government-owned, the right to conduct business in a particular market. For example, when a national railways transportation service is created by the government, in most cases they are granted a monopoly on the operation of passenger trains in the country. As a result, other firms are only able to offer passenger train services with the cooperation and/or permission of the government-owned provider.
Intellectual Property Protection: Extending intellectual property protection to a company in the form of patents and copyrights is yet another way in which monopolies are created. When a government does this, it is in fact giving a single company an exclusive right to provide a particular product / service to the market. Patents and copyrights work in providing owners of intellectual property with the right to act as an exclusive provider of a new product for a specific length of time. This creates a temporary monopoly in the market with regards to new products and services.
Natural Monopoly: A market may also become a monopoly simply because it may be more cost-effective for one company to serve the whole market than to have several smaller firms in competition with one another. A company with virtually unlimited economies of scale is referred to as a natural monopoly. Such firms become monopolies due to their position and size, which makes it impossible for new entrants in the market to compete price-wise. Natural monopolies are common in industries with high fixed costs and low marginal costs of operation such as providers of television, telephone, and internet services.
In this question, 'A single firm is very large' is not enough to tell whether this market is monopolistic.
