Answer
See below
Work Step by Step
Since $A$ has igenvalues $\lambda=1,1,3,3$, it will have four Jordan canonical forms, such as:
$$\begin{bmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 3 & 0\\
0 & 0 & 0 & 3
\end{bmatrix}$$
$$\begin{bmatrix}
1 & 1 & 0 & 0\\
0 & 1 & 0 & 0 \\
0 & 0 & 3 & 0 \\
0 & 0 & 0 & 3
\end{bmatrix}$$
$$\begin{bmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0 \\
0 & 0 & 3 & 1\\
0 & 0 & 0 & 3
\end{bmatrix}$$
$$\begin{bmatrix}
1 & 1 & 0 & 0\\
0 & 1 & 0 & 0 \\
0 & 0 & 3 & 1\\
0 & 0 & 0 & 3
\end{bmatrix}$$
