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The Elemental Materia needs to be paired with a green or red materia that has an innate element, and it changes effect depending on whether you equip it on a weapon or an armor.
On a weapon, it will add the paired materia's element to your physical attacks, which can be used to take advantage of an enemy's weakness.
On an armor, the damage from the paired materia's element will be reduced depending on the level of the blue Elemental Materia:
Level 1: half damage
Level 2: immunity (no damage)
Level 3: absorption (heals you instead)
The 4th Level of the Elemental Materia adds no additional effect and is just for multiplying the materia (all material create an additional copy of themselves once the materia reaches its max. level).