In this thesis, it is proved that the maximum number of 3 x 3 pure imaginary quaternionic solutions, T1,T2,…,Tp, of the Hurwitz matrix equations given by TiTj*+TjTi*={2I,if i=j, 0,otherwise. is 3. This thesis is divided into three chapters. There are some notations, definitions and background in Chapter 1. In Chapter 2, there are some lemmas and a theorem. In the theorem.it is shown that an n x n pure imaginary quaternionic unitary matrix is orthogonally congruent to a diagonal matrix. Chapter 3 consists of the main result. It is proved by contradiction that the maximum number of 3 x 3 pure imaginary quaternionic solutions of the Hurwitz matrix equations is 3.