Who wrote Luke and Acts?
Almost all scholars today (whatever they think about whether the Bible is historically reliable) believe that Luke's Gospel and the book of Acts were written by the same person.
(2) Acts chapter 1 verse 1 indicates that it is the sequel to a previous work, about 'everything Jesus began to do and teach until the day he ascended to heaven' - which is what Luke's Gospel is about.
(3) The language and style is very similar in Luke and Acts:
Stylistically and structurally, the Gospel of Luke and the Acts of the Apostles are so closely related that they have to be asssigned to the same author. This has been so extensively demonstrated by linguistic studies that it need not be elaborated here. (Expositors' Bible Commentary volume 9 page 238)
Why does it matter?
If the book of Acts is historically reliable (and it is), then this suggests that Luke's Gospel is also historically reliable. It is not proof, but it is suggestive.