Cramer's rule for a system of quaternion matrix equations with applications

In this paper, we investigate Cramer's rule for the general solution to the system of quaternion matrix equations A1XB1=C1,A2XB2=C2,and Cramer's rule for the general solution to the generalized Sylvester quaternion matrix equation AXB+CYD=E,respectively. As applications, we derive the determinantal expressions for the Hermitian solutions to some quaternion matrix equations. The findings of this paper extend some known results in the literature.