Is "Couple" a Plural Noun and is "Trio" a Singular Noun?

[A B]

Which of this Group ( sn) is correct?---
"The Couple IS fighting" "IS" = a Singular Verb for a Singular Noun
"The couple ARE fighting " " ARE ' = a Plural Verb for a Plural Noun
"The Trio IS playing " Singular Verb , Singular Noun
"The Trio ARE playing " Plural Verb , Plural Noun