Check the true statements below:

a. a number c is an eigenvalue of a if and only if the equation (a−ci)x=0 has a nontrivial solution x.
b. finding an eigenvector of a might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
c. to find the eigenvalues of a, reduce a to echelon form.
d. a matrix a is not invertible if and only if 0 is an eigenvalue of a.
e. if ax=λx for some vector x, then λ is an eigenvalue of a.