How do I prove / disprove "If a Matrix A is nonsingular, then the homogeneous system Ax=0 has a nontrivial solution?"
I know that if A is nonsingular, then exists and multiplying both sides of Ax=0 by gives so then and x=0. Therefore, the only solution to Ax=0 is x=0 so a nonsingular matrix never has a trivial solution to Ax=0.
Is this enough to disprove the statement?