# Math Help - homomorphism

1. ## homomorphism

Show that f(x,y)=x(-1)^y is homomorphism from the direct product group (positive) ×2 to the group *.

(need to show that f((a,b)(c,d))=f(a,b)f(c,d), is it right? but I can't get them equal to each other)

2. Take $(a,b),(c,d)\in \mathbb{R}^+ \times \mathbb{Z}_2$ then $f((a,b)(c,d))=ac(-1)^{b+d}=ac(-1)^b(-1)^d=a(-1)^bc(-1)^d=f((a,b))f((c,d))$

I'm assuming $\mathbb{R} ^+$ is the group of postitive real numbers with multiplication as operation.