I am stuck on the following problem that says:
If $\phi$ is a character of $G$ such that $\langle \phi,\phi \rangle=4$, then there exists a character $\chi$ of $G$ such that $\phi=2\chi$
I know that if $\phi=2\chi$ and $\langle \phi,\phi \rangle=4$ it implies $\langle 2\chi,2\chi \rangle=4$ and $\langle \chi,\chi \rangle=1$, so we conclude that $\chi$ is an irreducible character.
But, here I couldn't find any idea further to proceed,
Can someone help me out? Thanks in advance for your time!