Aban ibn Abdullah al-Bajali narrated from Abu Bakr ibn Hafs — and he is Ibn Umar ibn Sa'd ibn Abi Waqqas — from Ibn Umar: that he went out on the day of Eid, and he did not pray before it or after it, and he mentioned that the Prophet, peace and blessings be upon him, did the same. (1)

This is a good and authentic hadith.

Chapter 7: On the going out of women on the two Eids

547 - Ahmad ibn Mani' narrated to us, saying: Hushaym narrated to us, saying: Mansur — and he is Ibn Zadhan — informed us from Ibn Sirin, from Umm Atiyyah: that the Messenger of Allah, peace and blessings be upon him, used to bring out the virgins, the young unmarried women, the secluded women, and the menstruating women on the two Eids. As for the menstruating women, they would keep away from the place of prayer, and they would witness the supplication of the Muslims. One of them said: O Messenger of Allah, what if she does not have a jilbab? He said: "Let her sister lend her one of her jilbabs." (2)

548 - Ahmad ibn Mani' narrated to us, saying: Hushaym narrated to us, from Hisham ibn Hassan, from Hafsah bint Sirin, from Umm Atiyyah, similar to it. (3)

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(1) Authentic due to corroboration, and this chain is good, because of Aban. Ahmad recorded it in al-Musnad (5212), and see the rest of its citation there.
(2) Its chain is authentic. Al-Bukhari recorded it (324) and (351), Muslim (890), Abu Dawud (1136), (1137), and (1138), Ibn Majah (1307) and (1308), al-Nasa'i 1/193-194 and 3/180, and it is in al-Musnad (20793), and Sahih Ibn Hibban (2816).
(3) Authentic, and see the preceding one.