identity operator vs identity

identity operator and identity both are nouns.

Word	Noun	Adjective	Verb	Adverb
identity operator	Yes	No	No	No
identity	Yes	No	No	No

As nouns, identity operator and identity are synonyms defined as:

identity operator and identity: an operator that leaves unchanged the element on which it operates

Other synonyms of identity operator include identity element.

identity operator (noun)	identity (noun)
an operator that leaves unchanged the element on which it operates	the distinct personality of an individual regarded as a persisting entity
	exact sameness
	the individual characteristics by which a thing or person is recognized or known
	an operator that leaves unchanged the element on which it operates