-------------------------------------------------------------------------------- which is good between www.a.com/blog and blog.a.com which is better for seo?
www.a.com/blog would be better. Subdomains are treated as whole new websites and the weight of your main website would not be passed to your blog.
Oh, as as for the wordpress.com blogs, if you paid to use your own domain name, all you have to do is get your blog working on your own hosting or server and then changes the dns, all of the yoursite.wordpress.com stuff will redirect to yoursite.com just as it would've on their site. I still get hits from google images and some of the wordpress tags pages since I moved the blog to my own server.
if you use blog.a.com you will have to do everything realted to SEO etc all over again. This is because Google will treat it as a completely new domain. I would go for a.com/blog..
In my own experiences, if you want to build backlinks from your blog to your site, the 2nd one would be better. Or, you could even put your blog on a totally new domain. Thanks,
blog.com/newblog This is better and am damn sure about it..! Or Else Try Both and you can see this one going up and Subdomain just Snailin up..!