“Because we're templars!”
Mattrin is a former Templar. He joins The Inquisition after he was rescued during the Mage-Templar War.
Background
Mattrin was a new recruited templar, he along with Lysette, who was also a new templar recruit at that time, did not joined the templars to attend the Conclave meeting. After the Temple of Sacred Ashes was destroyed he survived when the Breach occurred there which killed all the mages and templars including the divine. He along with Lysette were the only survivors they were surrounded by demons but he along with Lysette survived with the aid of the Inquisition forces. Lysette felt indebted to them after saving her, she joined The Inquisition, Mattrin followed her and joined the Inquisition as well.
Involvement
After The Inquisitor wakes up Matrrin is found outside in the military camp standing with Lysette. He will be talking with Lysette telling her to see reason and that they can not stay with the Inquisition. Lysette asks why not can they stay. He says to her because their he and lysette are templars. Lysette will say what does that even mean. She will tell that should they fight amongst themselves instead of protecting the mages and she will say that should she and he declare independence on their own march off and do nothing. Mattrin will tell Lysette that it's better than staying with the Inquisition. Lysette will tell him that he is quick to dismiss the people who saved his life.
In In Your Heart Shall Burn, Mattrin can be seen near the stairs with Lysette.
After the destruction of Haven, he will occasionally be seen wandering around Skyhold.