Answer
Pure black dye is not permissible. Rasulullah (Sallallaahu Álayhi Wasallam) said, “There will be people who will come later (in my Ummah) and apply black dye. They will not even smell the fragrance of paradise.” (Abu Daawood). However, it is permissible for a Mujaahid (warrior) to apply black dye in order to give the impression of being young. (Jawahirul Fiqh vol2 pg421)
To dye the hair any other colour besides black e.g. Mehndi or Katm (type of grass) is permissible. This was the practice of Rasulullah (Sallallaahu Álayhi Wasallam) and the Sahaaba (Radhiyallaahu Ánhum). (Jawahirul Fiqh vol2 pg421)
and Allah Ta’ala Knows Best
Mufti Ebrahim Desai