Answer
False
Work Step by Step
Assume $J=\begin{bmatrix}
0 & 1\\
0 & 0
\end{bmatrix}$ is in Jordan canonical form.
Take $r=3$ we have $rJ=\begin{bmatrix}
0 & 3\\
0 & 0
\end{bmatrix}$
We can see that the matrix $r J$ is in Jordan canonical form.
Hence, the statement is false.
