1. The problem statement, all variables and given/known data Let A and B be n x n matrices and let C= A - B. Show that if Ax=Bx, and x does not equal zero, then C must be singular. 2. Relevant equations 3. The attempt at a solution Ax-Bx=0 x(A-B)=0 x(C)=0 So, Cx=0 Does that mean C is singular?