It is a Torah commandment to eat matza on the night of the 15th of the month of Nisan, as it says, “In the evening, you shall eat matzot” (Shemot 12:18). Even though the Torah also says, “you shall eat matzot for seven days” (ibid. 12:15), the Sages inferred, based on the rules for interpreting the Torah, that the Torah does not mean to command us to eat matzot all seven days. Rather, the intent is that matza is the staple food that we eat on Pesaḥ in lieu of bread. However, one who wants to live off of fruits, vegetables, meat, and dairy products may do so.
The simple meaning of this is that one who eats matzot all seven days of Pesaḥ does not thereby fulfill a mitzva. This is what the Sages meant when they said (Pesaḥim 120a) that eating matza during the seven days is “optional” (“reshut”). Yet many leading halakhic authorities have written that although eating matza is obligatory only at the Seder, and indeed that is why the Sages instituted the special blessing over the eating of matza at the Seder only, nevertheless one who eats matza on the other days of Pesaḥ still fulfills a mitzva, even if it is not obligatory. In this view, the Sages referred to eating matza on the remaining days of Pesaḥ as a “reshut” only by way of contrast with the obligation to eat matza on the night of the 15th. According to this view, the verse “you shall eat matzot for seven days” retains its simple meaning. This is how Ibn Ezra and Ḥizkuni explained the verse, this is implied by a statement by Rosh, and this was the practice of the Vilna Gaon. However, even they maintained that the mitzva consists of eating a kezayit (olive’s bulk) of matza at each meal, and that eating more does not add to the mitzva.
Most Rishonim and Aḥaronim do not mention any mitzva associated with eating matza during the seven days of Pesaḥ, implying that there is in fact no such mitzva. However, many Rishonim and Aḥaronim do actually mention such a mitzva, including: Ibn Ezra on Shemot 23:15, Ḥizkuni on Shemot 12:15, and Responsa Rosh 3:23 citing the Ge’onim that one does not wear tefillin on Ḥol Ha-mo’ed Pesaḥ, since there is already a “sign” on Pesaḥ, namely, eating matza. So states MB 475:45 in the name of Gra (Ma’aseh Rav §185).