Why does character of identity element always positive integer?

I'm a chemist who is interested in mathematics. One of the subject that I'm interested in is group theory and representation theory, because of its application in chemistry.

I was looking at character tables and realize that the characters of identity element is always a positive integer (i.e. in $$Sym(3)$$ the character for identity element is 1 and 2, in $$Sym(4)$$ the character for identity element is 1, 2, and 3, etc.).

Is there any reason for why this is true?
• The character of the identity element is the trace of the identity matrix, i.e. the dimension (the "degree") of the representation. Apr 15, 2023 at 21:52
• The trace of the identity for any finite dimensional vector space is the sum of $1$s. Apr 15, 2023 at 21:52
• Ah, I see. Thank you. Apr 15, 2023 at 22:06
• @AnneBauval Can you make that into an answer? Although it is trivial, we do not want answers to be lost in comments.
– Pedro
Apr 17, 2023 at 8:48
• @AnneBauval No problem.
– Pedro
Apr 17, 2023 at 9:06