Matrices and Determinants

Given, AX=B and CX=D and AX=B has unique solution D and CX=D has unique solution B.
Since, X=D is the unique solution of AX=B
∴‌‌AD=B
And, X=B is the unique solution of CX=D,
∴‌‌CB=D⇒B=C−1D
From Eq. (i) and (ii),
AD=C−1D
(A−C−1)D=0
So, the solution of (A−C−1)X=0 is D