Answer
False
Work Step by Step
We have $J_1=\begin{bmatrix}
0 & 1\\
0 & 0
\end{bmatrix}$ and $J_2=J_1=\begin{bmatrix}
0 & 1\\
0 & 0
\end{bmatrix}$ are $n \times n$ matrices in Jordan canonical
form.
Obtain: $J_1+J_2=J_1=\begin{bmatrix}
0 & 2\\
0 & 0
\end{bmatrix}$
We can notice that the matrix $J_1+J_2$ is not in Jordan canonical form.
Hence, the statement is false.
