So I'm given the following definition:
$h(g)p(z)=p(g^{-1}z)$ where g is an element of $SL(3,\mathbb{C})$, $p$ is in the vector space of homogenous complex polynomials of $3$ variables and $z$ is in $\mathbb{C}^3$.
What I'm having trouble showing is that mapping $g$ to $h(g)$ is a group homomorphism. Namely, I know that $h(ab)p(z)=p(b^{-1}a^{-1}z)$, but I can't seem to make sense that $h(a)(h(b)(p(z))$ is not $p(a^{-1}b^{-1}z)$.
This is probably trivial, so condescending replies are welcome!