「」「」
"She likes music." "So do I."
Literal
"She [topic-は] music [subject-が] liked [copula-だ]" "I [also-も] so [copula-だ]"
私もそうだ ('I am also so / me too') is the standard way to agree that something applies to you as well. そう here is a pro-form standing in for 'the same state.' も is the inclusive 'also/too' particle. Short, efficient, and very common in conversation.