1. Define \$$f_2\circ f_1:=f_3\$$. Entries will be of the form \$$\text{Top}\circ\text{Side}\$$, or \$$NA\$$ if no such composition is possible.

$$\begin{array}{ c l c c c c c c} \text{Hom}_\mathbf{3} & f_1 & f_2 & f_3 & \text{id}_1 & \text{id}_2 & \text{id}_3 \\\\ \hline f_1 & NA & f_3 & NA & NA & f_1 & NA \\\\ f_2 & NA & NA & NA & NA & NA & f_2 \\\\ f_3 & NA & NA & NA & NA & NA & f_3 \\\\ \text{id}_1 & f_1 & NA & f_3 & \text{id}_1 & NA & NA \\\\ \text{id}_2 & NA & f_2 & NA & NA & \text{id}_2 & NA \\\\ \text{id}_3 & NA & NA & NA & NA & NA & \text{id}_3\end{array}$$

2. The identities are on the diagonal. This is because the only morphisms with inverses in this category are the identity morphisms.