I have a problem and a proposed solution. Please tell me if I'm correct.
Problem: For A,B real matrices, prove that if there is a solution in the complex numbers then there is also a real solution.
Solution: A and B are real matrices. Therefore, they are not defined over the complex plane, and a solution in C is not possible for the system AX=B. Hence, the "if" part is false by default and the "then" part is always true, making the implication always true and rendering the problem statement as proven.