My mother has a question. She was asking that can a woman perform Wudu without the Hijab (or without covering her head) and when she is done with Wudu she can cover her head.
She do Wudu alone by the way!
Is this permissible?
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Just to make something clear:
A woman should hide more than her head or hair from the view of non-mahrams. So if a woman thinks she can make wudu' (ablution) in front of non-mahrams, but can't take of her hijab, that's a wrong thinking as to make wudu' she also would need to show her forearms (which are 'awrah too) etc. So women are asked to try their best to perform wudu' in a place non-mahrams can't see them.
Now back to your question:
Basically she could wipe over head cover under some conditons like if it is too cold. Else wudu' wouldn't be done correctly.
So taking off the hijab is rather necessary to make a correct and valid wudu'. As Allah ordered to wipe over our heads (inculding the hair) -not on the head covers- in the verse ordering and explaining wudu' (5:6):
O you who have believed, when you rise to [perform] prayer, wash your faces and your forearms to the elbows and wipe over your heads and wash your feet to the ankles. . ..
I will try to elaborate this answer to cover the views of the different madhabs as the hanbali school seems to disagree.
See also this fatwa on islamqa #72391.