In invocations like Agonizing Blast, PHB states
Prerequisite: Eldritch Blast cantrip
When you cast Eldritch blast, add your Charisma modifier to the damage it deals on hit.
However on invocations like Armor of Shadows, PHB states
You can cast Mage Armor on yourself at will, without expending a spell slot or material components.
My issue is while Agonizing Blast explicitly requires the spell in the first place to work, Armor of Shadows doesn't state you need to know the spell before gaining the invocation. Will gaining Armor of Shadows give you Mage Armor for free?