linear algebra - Are the following two matrices similar?

Suppose that

1) we do not know the theory of lambda-matrix;

2) we can not see the transition matrix directly (use elementary tranformations).

How can we deduce that the following two matrices are similar? (What we only know is that they have the same eigenvalues, eigenvectors, rank, determinant)

$$ \begin{pmatrix} 1&1&0\\ 0&0&1\\ 0&0&0 \end{pmatrix},\quad \begin{pmatrix} 1&1&1\\ 0&0&1\\ 0&0&0 \end{pmatrix} $$