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
