I'm studying the book "Spin Geometry" by Lawson and Michelson. In the proof of proposition 4.2 they say (with no proof) that there is this algebra isomorphism
$$Hom_{\mathbb{C}}(\mathbb{H},\mathbb{H})\simeq\mathbb{C}(2)$$
where $\mathbb{H}$ are quaternions and $\mathbb{C(2)}$ are 2 by 2 complex matrices.
I can't find anywhere a proof of this fact, can you help me?