Determinantal representation of the generalized inverses over the quaternion skew field with applications

In this paper, we establish some new determinantal representations of the generalized inverses ArT1,S1(2),AlT2,S2(2) and A(T1,T2),(S1,S2)(2) over the quaternion skew field by the theory of the column and row determinants. In addition, we derive a condensed Cramer rule for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature.