Here are the Merriam-Webster definitions and Subject, while having more uses than Subject Matter, does seem to be a synonym. (see the definition example below)
All of this could have been answered by a quick dictionary search.
Object 4 : a thing that forms an element of or constitutes the subject matter of an investigation or science objects of study
subject matter: matter presented for consideration in discussion, thought, or study
subject 3 d (1) : something concerning which something is said or done the subject of the essay (2) : something represented or indicated in a work of art
e (1) : the term of a logical proposition that denotes the entity of which something is affirmed or denied; also : the entity denoted (2) : a word or word group denoting that of which something is predicated