is the phrase( as a matter of fact)a transitional word?

It's wordy, but could be.

http://leo.stcloudstate.edu/style/transitioncues.html

Yes, the phrase "as a matter of fact" can be considered a transitional word or phrase. Transitional words and phrases are used to connect ideas, add information, or introduce examples in a sentence or paragraph.

To confirm this, you can consult a reliable source, such as a grammar or writing guide. One well-known resource for understanding transitional words and phrases is "The Elements of Style" by William Strunk Jr. and E. B. White. This book provides guidelines and explanations for improving writing style and usage.

Another convenient way to determine if "as a matter of fact" is a transitional word is to consult an online resource such as a dictionary or a writing guide website. These sources often categorize transitional words and phrases, making it easy to identify them.

Remember, it's always a good practice to cross-reference information from multiple sources to ensure accuracy and to develop a comprehensive understanding of transitional words and how they are used in writing.