Al-Imaam Abdul-Azeez Ibn Abdillaah Ibn Baaz (may Allaah have mercy upon him) answered this question:
"Salaatul-Eid is a communal obligation with many of the scholars. It is permissible for some individuals to remain behind and not attend. However, the person being present participating with his/her Muslim brothers/sisters is an emphasized Sunnah, which is not befitting to leave off ,except with a legislated excuse. Some of the scholars hold the position that Salaatul-Eid is an individual obligation similar to Salaatul-Jumu'ah. Therefore, it would not be permissible for the one who is held accountable from amongst the men, who are free and residents to remain behind from making the prayer. This statement is the most apparent from the evidences and closet to that which is correct. It is from the Sunnah for the women to be present along with them observing the proper Hijaab and covering without perfume. This is based upon that which is established in the Saheehayn (Bukhaari and Muslim) on the authority of Umm 'Atiyyah (may Allaah be pleased with her) she said:
"Salaatul-Eid is a communal obligation with many of the scholars. It is permissible for some individuals to remain behind and not attend. However, the person being present participating with his/her Muslim brothers/sisters is an emphasized Sunnah, which is not befitting to leave off ,except with a legislated excuse. Some of the scholars hold the position that Salaatul-Eid is an individual obligation similar to Salaatul-Jumu'ah. Therefore, it would not be permissible for the one who is held accountable from amongst the men, who are free and residents to remain behind from making the prayer. This statement is the most apparent from the evidences and closet to that which is correct. It is from the Sunnah for the women to be present along with them observing the proper Hijaab and covering without perfume. This is based upon that which is established in the Saheehayn (Bukhaari and Muslim) on the authority of Umm 'Atiyyah (may Allaah be pleased with her) she said:
"We were commanded to come out to the two Eids, the young, unmarried and the menstruating women in order to witness the good, the call of the Muslims and the menstruating women were to keep away from the prayer."
In some wordings it was mentioned:
"One of them said: Oh Messenger of Allaah, (what are we to do if) one of us doesn't have a garment to come out in?"
The Prophet (sallallaahu alayhi wa sallam) said:
"Let her sister cover her from her garments."
There is no doubt that this indicates the emphasis that is placed on the women coming out for the Salaatul-Eidayn and to witness the good and the call of the Muslims.
Source: Fataawa al-Mar-ah al-Muslimah pg. 258
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