Let $A\in M_{n}(\mathbb{H})$ be a matrix with complex spectrum where $ \mathbb{H} $ is quaternions set. I want to prove $A$ is triangularizable. In fact, I want to prove every quaternionic matrix is triangularizable.
To this end, since minimal polynomial of $A$ exists, so it's enough to show that its minimal polynomial is reducible.
I want use contradiction. If the minimal polynomial is irreducible, then what's the form? And How do I get a contradiction?