What Proof is There That Hijab is Mandatory?

The following verse commands women to cover their zeenah (the term for the parts of a woman which are considered her beautification):

˹O Prophet!˺ Tell the believing men to lower their gaze and guard their chastity. That is purer for them. Surely Allah is All-Aware of what they do. And tell the believing women to lower their gaze and guard their chastity, and not to reveal their zeenah except what normally appears. Let them draw their veils over their chests, and not reveal their ˹hidden˺ adornments except to their husbands, their fathers, their fathers-in-law, their sons, their stepsons, their brothers, their brothers’ sons or sisters’ sons, their fellow women, those ˹bondwomen˺ in their possession, male attendants with no desire, or children who are still unaware of women’s nakedness. Let them not stomp their feet, drawing attention to their hidden adornments. Turn to Allah in repentance all together, O  believers, so that you may be successful. (24:30-31)

Hijab in the Qur’an; Hijab: The Muslim Woman's Dress, Islamic or Cultural?

The following are two hadith, among many others, which are authentic and prove the obligation of hijab:

A number of our people have narrated from Ahmad ibn Muhammad ibn ‘Isa from ibn Mahbub from Jamil ibn Darraj from Fudayl ibn Yasar who has said the following: “This is concerning my question before abu ‘ Abd Allah (a.s), about the arms of women if they are of beautification about which Allah, most Blessed, most High, has said, . . they must not expose their beauty except for their husband.’ (24:32) He (the Imam) said, ’Yes, whatever must be covered with the scarf is of their beauty and whatever is above their bracelet is of their beauty.’” (Al Kafi)

Muhammad b. Ismail from al-Fadhl b. Shadan AND Abu Ali al-Ash`ari from Muhammad b. Abd al-Jabbar all together from Safwan b. Yahya from Abd al-Rahman b. al-Hajjaj who said: I asked Aba Ibrahim عليه السلام about a girl who has not attained puberty – when is it incumbent on her to cover her head from the one one with whom she does not share any relation? and when is it obligatory on her to veil her head fully in the prayer? He said: she does not have to cover her head until the prayer starts becoming prohibited on her [i.e. she begins menstruating]. (Al Kafi)

Further discussion of these hadith can be found in "Aurah of a Woman.