Answer
False
Work Step by Step
We have $J_1=\begin{bmatrix}
1 & 1 \\
0 & 1
\end{bmatrix}$ and $J_2=\begin{bmatrix}
1 & 1 \\
0 & 1
\end{bmatrix}$ are $n \times n$ matrices in Jordan canonical form
Obtain: $J_1J_2=\begin{bmatrix}
1 & 2 \\
0 & 1
\end{bmatrix}$
We can notice $J_1J_2$ is in Jordan canonical form.
