Let V be a finite dimensional complex vector space and T be the linear operator of V. Prove that the following are equivalent
a V has a basis consisting of eigenvectors of T.
b T can be represented by a diagonal matrix.
c all the eigenvalues of T have multiplicity one.
d. the Characteristic polynomial of T equals the minimal polynomial of T.
Not really applicable
The Attempt at a Solution
Ok so I proved A implies B, However, I feel that B does not imply C.
I just want to see if my argument is valid. because the identity matrix, is definitely diaganol however, it does not have a multiplicity of One. Can I assume wlog that T has distinct eigenvalues along the main diaganol?