The phrase as a matter of fact is similar to in fact and is used to emphasis a piece of information, usually in order to clarify a point that was just made, either to confirm it or negate it. The point can be made in a conversation or just expanding on something the speaker said.
To be matter-of-fact about something is to be without emotion and clear. Something can be a matter-of-fact if it’s true and not up for a debate.
The idiom the fact of the matter is almost always used as an introductory phrase in a sentence. It means that whatever follows is the truth or sometimes it is the main point of discussion in an argument.
We have a website for selling books, but it only draws a small percentage of readers. As a matter of fact, they seem to use it more to select titles online, but then they come to buy the actual book here at the shop. [The Guardian]
“The fact of the matter is that the younger audience, the first audience that comes into ‘Infinity,’ is more familiar with Episodes 1-3,” said Disney Interactive executive John Vignocchi, explaining why Han and Luke and Leia aren’t in the starter packs. [Los Angeles Times]
Pulis was often though of as a ‘boring’ manager with negative tactics, but the fact of the matter was that he got the job done and managed to produce results. [Plymouth Herald]