Tensor product of irreducible representation and one-dimensional representation is irreducible

Statement
Suppose $$G$$ is a group and $$K$$ is a field. Suppose $$\rho_1:G \to GL(V_1)$$ is an irreducible linear representation] of $G$ over $K$ and $\rho_2: G \to GL(V_2)$ is a one-dimensional linear representation of $G$ over $K$. Then, the [[tensor product of linear representations $$\rho_1 \otimes \rho_2$$ is an irreducible linear representation of $$G$$ over $$K$$. Also, this tensor product is projectively equivalent to $$\rho_1$$.