Contragredient representation of finite group equals composite with complex conjugation

Statement
Suppose $$K$$ is a field of characteristic zero that is a subfield of the field of complex numbers. Suppose that $$K$$ is closed under the operation of complex conjugation operation.

Suppose $$G$$ is a finite group and $$\rho:G \to GL(n,K)$$ is a finite-dimensional linear representation.

Then, the contragredient representation to $$\rho$$ is equivalent as a linear representation to the composite of complex conjugation with $$\rho$$. 

Facts used

 * 1) uses::Character determines representation in characteristic zero
 * 2) uses::Trace of inverse is complex conjugate of trace

Proof
The proof basically follows by combining Facts (1) and (2). Fact (2) shows that the contragredient representation has the same character as the composite with complex conjugation. Fact (1) then forces the representations to themselves be equivalent.