Gemara

Rava: Nowadays Matzah is a Mitzvah mid'Oraisa; Maror is only mid'Rabanan.

Question: Surely, Maror is mid'Rabanan because "Al Matzos u'Morerim Yochluhu". It is mid'Oraisa only when there is Korban Pesach; the same applies to Matzah!

Answer: Another verse teaches "Ba'Erev Tochlu Matzos" (in any case).

Rav Acha bar Yakov: Both of them are mid'Rabanan today.

Question: But it says "Ba'Erev Tochlu Matzos"!

Answer: That obligates one who is Tamei or b'Derech Rechokah (when the Mikdash stands) to eat Matzah. One might have thought that since they do not eat Pesach, they need not eat Matzah and Maror. The verse teaches that this is not so.

Ran: The Gemara mentions Maror along with Matzah, but really, (mid'Oraisa) the only Mitzvah to eat Maror is with Pesach.

Support (for Rava - Beraisa): "Sheshes Yomim Tochal Matzos uva'Yom ha'Shevi'i Atzeres" - just like eating Matzah on the seventh day is Reshus (not obligatory), also six days (and a half, i.e. after the first night).

This was part of a Kelal ("Shiv'as Yomim Tochal Matzos"), and the Torah taught about it by itself; in every such case we learn to the entire Kelal.

Suggestion: Perhaps even the first night is Reshus!

Rejection: "Al Matzos u'Merorim Yochluhu".

Question: Perhaps that is only when the Mikdash stands - what is the source when the Mikdash does not stand?

Answer: "Ba'Erev Tochal Matzos" - it is obligatory.

28b - Beraisa - R. Yehudah: We learn that one who eats Chametz after six hours transgresses a Lav from "Lo Sochal Alav Chametz";

R. Shimon disagrees - it says "Lo Sochal Alav Chametz Shiv'as Yomim Tochal Alav Matzos" (Chametz is forbidden only from when Matzos must be eaten, at night)!

R. Yehudah holds that the verse equates the Mitzvah to eat Matzah to the Isur Chametz to teach that the Mitzvah applies in all generations.

R. Shimon learns this from "Ba'Erev Tochlu Matzos".

Shabbos 131b (Beraisa - R. Eliezer): Matzah and all its Machshirim override Shabbos.

Question: What is his source?

He cannot learn from Sukah, for Sukah applies at night like during the day!

Answer: He learns from a Gezerah Shavah "Chamishah Asar-Chamishah Asar" from Sukah.

Rishonim

The Rif and Rosh (10:37) bring Rava, the question against him and its answer, and the Beraisa supporting him.

Rambam (Hilchos Chametz u'Matzah 6:1): It is a Mitzvah mid'Oraisa to eat Matzah on the night of the 15th - "Ba'Erev Tochal Matzos". This applies elsewhere, in all generations. The Mitzvah does not depend on Korban Pesach. The Mitzvah applies all night. During the rest of Pesach eating Matzah is Reshus; one may eat Matzah, rice, millet, parched grain or produce. The only Chiyuv to eat Matzah is on the 15th.

R. Mano'ach: There is no Mitzvah at all to eat after the first night.

Rambam (ibid.): Once one ate a k'Zayis he fulfilled his obligation.

Rosh (10:38): There are two Stam Mishnayos like R. Elazar ben Azaryah, which suggests that the Halachah follows him. However, there is also a Stam Mishnah like R. Akiva, and two Stam Mishnayos are no stronger than one! Also, the Stam like R. Akiva teaches Halachos Pesukos (that are also taught elsewhere), so it is more authoritative. Nevertheless it is proper to be stringent like R. Elazar ben Azaryah; perhaps R. Akiva would agree that one must eat before midnight, lest he neglect to eat the entire night. R. Tam was stringent like this.

Rebuttal (R. Mano'ach ibid.): Regarding Kodshim (that the Torah permits until dawn) we are stringent to eat before midnight, for if one will eat after dawn he is Chayav Kares. There is no Isur to eat Matzah after dawn, so we need not decree to eat before midnight.

Ran (DH Garsinan): Since we do not know which Stam Mishnah Rebbi taught last, we must be stringent about the Safek and eat Afikoman before midnight. Tosfos is stringent to finish even Hallel before midnight. Some are lenient and rely on the rule that the Halachah follows R. Akiva against any colleague; this is why Rava said 'nowadays, according to R. Elazar ben Azaryah', and not simply 'nowadays...' It is not proper to be so lenient.

Question (Tosfos Shabbos 131b DH v'I): Why does the Gemara (Shabbos 131b) say 'he cannot learn Matzah from Sukah, for Sukah applies at night like during the day'? The primary Mitzvah to eat Matzah is at night!

Answer (Tosfos ha'Rosh Shabbos 131b DH v'Chol): Indeed, these words are for parallel structure with the previous Gemara 'he cannot learn Lulav from Sukah, for Sukah applies at night like during the day.' Sukah applies at night and during the day means, we bless 'Leshev ba'Sukah' throughout all of Sukos, whereas we bless 'Al Achilas Matzah' only on the first night.

Note: Berachos (except for Birkas ha'Torah and Birkas ha'Mazon) are mid'Rabanan, this cannot refute a Limud for a mid'Oraisa law! Tosfos ha'Rosh must mean (like Tosfos) that Sukah is a (voluntary) Mitzvah throughout Sukos, whereas Matzah is not a Mitzvah at all after the first night.

Question (Ba'al ha'Ma'or Pesachim 26b b'Sof): A Gezeirah Shavah equates Matzah and Sukah. One must eat a k'Zayis of bread in the Sukah on the first night; afterwards, it is Reshus. Why do we bless 'Leshev ba'Sukah' throughout all of Sukos, but 'Al Achilas Matzah' only for the Chiyuv?

Answer (Ba'al ha'Ma'or): A person need not eat Matzah after the first night; he can survive a week without Matzah. However, one cannot go even three days without sleeping, and sleeping must be in a Sukah. This is the meaning of 'he cannot learn Matzah from Sukah, for Sukah applies at night like during the day'.

Note: If the Ba'al ha'Ma'or held that Sukah is a Mitzvah throughout Sukos, but Matzah is not a Mitzvah after the first night, he has no question! Rather, he must hold that also Matzah is a (voluntary) Mitzvah the entire Regel.

Poskim

Shulchan Aruch (OC 475:7): The Chiyuv to eat Matzah is only on the first night...a k'Zayis suffices.

Magen Avraham (16): One must eat bread every day (to honor the festival), but for this Matzah Ashirah suffices.

Mishnah Berurah (45): The Gra says that it is a Mitzvah every time one eats Matzah during Pesach, just it is not obligatory.

Aruch ha'Shulchan (18): I have a tradition that even though there is no obligation to eat Matzah after the first night, one who eats fulfills a Mitzvah.