As a matter of fact and Indeed

As a matter of fact adverb - In reality or actuality.

Indeed is a synonym for as a matter of fact in really topic. In some cases you can use "Indeed" instead the phrase "As a matter of fact" as an adverb or an adjective, when it comes to topics like actually, existent, without a doubt.

Indeed adverb - Without any question.

As a matter of fact is a synonym for indeed in actually topic. You can use "As a matter of fact" instead the word "Indeed" as an adverb or an adjective, if it concerns topics such as as expected.