<PRE><B>Question 624750</B>
(A^-1 X)^-1 =A (B^-1 A)^-1


(A^-1 X)^-1(A^-1 X) =(A (B^-1 A)^-1)(A^-1 X)


I =(A (B^-1 A)^-1)(A^-1 X)


A^-1 * I =(A^-1 A (B^-1 A)^-1)(A^-1 X)


A^-1 = ((B^-1 A)^-1)(A^-1 X)


(B^-1 A)A^-1 = ((B^-1 A)(B^-1 A)^-1)(A^-1 X)


(B^-1 A)A^-1 = A^-1 X


A(B^-1 A)A^-1 = A*A^-1 X


A(B^-1 A)A^-1 = X


X = A(B^-1 A)A^-1


So the solution is X = A(B^-1 A)A^-1</PRE>