Posteriod distribution of Normal Inverse Gamma model

Question

I want to derive the posterior distribution (without the normalizing constant) of: $$p(\mu,\sigma^2)=p(\mu| \sigma^2)p(\sigma^2)$$ with $$\mu|\sigma^2 \sim N(2,1.7^2\sigma^2) \ \ \text{and} \ \ \sigma^2\sim IG(10,20)$$ IG denotes an inverse-gamma distribution. I know the solution is an Inverse gamma distribution but I need to find out the rate and scale parameters. Does anyone know how to derive the posterior?