Show that for each nonzero number $a$, $a J(k)$ is similar to $J(k)$.
Show that if $a_1, a_2, \ldots, a_d$ are $d$ nonzero complex numbers and if $k_1,k_2,\ldots,k_d$ are arbitrary positive integers, then the block matrices
\begin{bmatrix} a_1 J(k_1) & 0 & \cdots & 0\\ 0 & a_2 J(k_2) & \cdots & 0\\ \vdots & & \ddots & \vdots\\ 0 & 0 & \cdots & a_d J(k_d)\end{bmatrix}
and \begin{bmatrix} J(k_1) & 0 & \cdots & 0\\ 0 & J(k_2) & \cdots & 0\\ \vdots & & \ddots & \vdots\\ 0 & 0 & \cdots & J(k_d)\end{bmatrix} are similar.
So far I have $J(k)$ denoted as the Jordan cell $J(0,k)$, i.e., $J(k)=J(0,k)= \begin{bmatrix} 0 & 1 & 0 & \cdots & 0\\ 0 & 0 & 1 & \cdots & 0\\ \vdots & & & \ddots & \vdots\\ 0 & 0 & \cdots & \ddots & 1\\ 0 & 0 & 0 & \cdots & 0\end{bmatrix}$
I am clueless after that, please help!