Find infinitely many homomorphism from $GL\_2(\mathbb Q)$ to $\mathbb Q^\*$. Here $\mathbb Q^\*$ means the multiplicative group of nonzero rational numbers.

**My attempt:** An example is the determinant function, which is a homomorphism satisfying the statement given. But I don't see how can I make any progress by knowing this fact and generate an infinite number of homomorphisms. I thought it'll be a good idea to find all the normal subgroups of $GL\_2(\Bbb Q)$, but I can't think of any other than the $SL\_2(\Bbb Q)$.

Help will be really appreciated. Thanks.