Hajj is obligatory for women as it is for men

In a talk recently, the speaker said that it is not fard for women to perform Hajj whereas it is only fard for men. Please could you state any ahadith or ayaah as evidence for this statement. If this statement is wrong, please could you also state the relevant ahadith/ayaah.

Praise be to Allaah.
Hajj is fard ‘ayn (an individual obligation) which every Muslim who is accountable and is able to do it must do once in a lifetime. It is one of the pillars of Islam, an obligation which is proven to be so in the Qur’aan and Sunnah, and by scholarly consensus.

1 – In the Qur’aan, Allaah says (interpretation of the meaning):

“And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allaah, those who can afford the expenses (for one’s conveyance, provision and residence); and whoever disbelieves [i.e. denies Hajj (pilgrimage to Makkah), then he is a disbeliever of Allaah], then Allaah stands not in need of any of the ‘Aalameen (mankind, jinn and all that exists)”

[Aal ‘Imraan 3:97]

This aayah clearly states that it is obligatory. When the Qur’aan says “a duty that mankind owes to Allaah” this implies that it is obligatory and compulsory. This is the evidence that it is fard. Indeed, we find that the Qur’aan emphatically states that it is obligatory, in the phrase “and whoever disbelieves [i.e. denies Hajj (pilgrimage to Makkah), then he is a disbeliever of Allaah], then Allaah stands not in need of any of the ‘Aalameen (mankind, jinn and all that exists).” Allaah describes going against this obligation as kufr or disbelief. This context shows that failing to do Hajj is not the action of a Muslim, rather it is the action of a non-Muslim.
2 – In the Sunnah, there is the hadeeth of Ibn ‘Umar (may Allaah be pleased with him) according to which the Prophet (peace and blessings of Allaah be upon him) said: “Islam is built on five (pillars): the testimony that there is no god except Allaah and that Muhammad is the Messenger of Allaah; establishing regular prayer; paying zakaah; fasting Ramadaan; and Hajj.”

The phrase “Islam is built…” indicates that Hajj is one of the pillars of Islam. Muslim narrated that Abu Hurayrah said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) gave a sermon and said to us: ‘O people, Allaah has enjoined Hajj upon you so perform Hajj.’ A man said, ‘Every year, O Messenger of Allaah?’ He did not answer until the man had asked it three times, then the Messenger of Allaah (peace and blessings of Allaah be upon him) said, ‘If I had said yes, it would have become obligatory and you are not able to do that.’” And there are so many ahaadeeth concerning that that it reaches the level of tawaatur which means that this obligation is something certain and definite.

 3 – With regard to ijmaa’ or scholarly consensus, the ummah is unanimously agreed that Hajj once in a lifetime is obligatory for the one who is able to do it. This is something which is well known and no Muslim has any excuse for not knowing it, and the one who denies it is a kaafir.

 Al-Mawsoo’ah al-Fiqhiyyah, part 17, p. 23

 Al-Nawawi said: They are unanimously agreed that Hajj is obligatory upon a woman if she is able to do it. Sharh Saheeh Muslim.