A mana ability is an ability that produces mana, not an ability that costs mana.

Damping Matrix’s ability affects only artifacts and creatures on the battlefield. Activated abilities that work in other zones (such as bloodrush or unearth) can still be activated. Triggered abilities (starting with “when,” “whenever,” or “at”) are unaffected.

Activated abilities contain a colon. They’re generally written “[Cost]: [Effect].” Some keyword abilities, such as equip, are activated abilities and will have colons in their reminder text.