A company has $6$ departments, and there are communication links between some pairs of departments. If the communication pattern is represented by an adjacency matrix, where a $1$ indicates a link and $0$ indicates no link, create the adjacency matrix for the following connections:

$$ Department $1$ communicates with Department $3$ and $4.$

$$ Department $2$ communicates with Department $1,3,$ and $5.$

$$ Department $4$ communicates with Department $6.$