A is an n times n matrix. Check the true statements below: If Ax = lambda x for some vector x , then lambda is an eigenvalue of A . A number c is an eigenvalue of A if and only if the equation (A-cI)x=0 has a nontrivial solution x . Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. To find the eigenvalues of A , reduce A to echelon form. A matrix A is not invertible if and only if 0 is an eigenvalue of A .