In this paper, we investigate the algebraic properties of Hurwitz split quaternions through their matrix representations. We construct the 4 4 left and right matrix representations and demonstrate that they have a specific block structure. Furthermore, we establish that the left representation is a homomorphism, while the right representation is an anti-homomorphism. Finally, we investigate certain properties of these matrices, proving that the trace is always an even integer and the determinant corresponds to the square of the split quaternion norm.
Neslihan Ayşen Özbay (Mon,) studied this question.