Questions & Answers about Innkaupakarfan er full af eplum.
Because Icelandic commonly expresses the with a definite suffix attached to the noun.
- innkaupakarfa = a shopping basket (indefinite)
- innkaupakarfan = the shopping basket (definite)
The -n (or -inn/-in/-ið) ending changes depending on gender, case, and declension type. Here it’s feminine singular nominative definite, which can surface as -an for this noun’s pattern.
It matters because gender controls endings on the noun (and agreement on adjectives/pronouns). karfa is a common feminine noun pattern in Icelandic (many nouns ending in -a are feminine, though not all). In this sentence, feminine gender is why the definite ending looks the way it does and why you’d use forms like full (not a feminine form) in the predicate in a specific way (see other questions).