Is it possible for a mineral to have a prismatic habit with out having any cleavagewhy or why not?

Yes, a mineral can exhibit a prismatic habit without having any cleavage. Prismatic habit refers to the elongated, column-like shape of the mineral's crystals, which can occur regardless of the internal atomic structure. Cleavage, on the other hand, is the tendency of a mineral to break along specific planes of weakness in its crystal structure. Some minerals may develop a prismatic form due to their growth conditions while lacking cleavable planes, resulting in a fracture instead of cleavage.