Find all Jordan canonical forms of 2 x 2, 3 x 3 and 4 x 4 matrices over C.

Question

Can someone walk me through understanding this question/solution to it? On the one hand, I'm thinking something simple like (for the $2 \times 2$ case):

\begin{bmatrix} \alpha & 1 \\ 0 & \beta \\ \end{bmatrix}

and

\begin{bmatrix} \alpha & 0 \\ 0 & \beta \\ \end{bmatrix}

Since there's no other way to be in JCF for a $2 \times 2$ matrix. On the other hand, this seems to naive.