Matthew goes to considerable lengths in his biography of the life of Jesus in chapters 5-10 to demonstrate the Christ's authority.
The Sermon on the Mount, among many things, shows Christ's authority over the Law, and his authority to teach.
He has authority over incurable disease (8:1-4)
Authority of command, to heal from afar (8:5-13)
Authority over spirits and demons (8:14-17)
Authority over the weather (8:23-27)
Authority over a multiplicity of demons, and over animals (8:28-34)
And finally, we come to chapter 9, where the description of Jesus' authority culminates in his authority to forgive sins.
It is also worth noting that in the very next chapter Jesus delegates authority over demons, sickness, and disease to his disciples, and it is in that context that they are first called "apostles."