To check your brand's authority on Moz for free, you can use their "Brand Authority Checker" tool. However, it seems that this tool is not directly available as a free resource.

But, you can use the "Authority Score" feature to get an estimate of your brand's authority. To do this:

1. Go to Moz.com and sign in to your account.
2. Click on the "Brand" tab at the top navigation bar.
3. Enter your domain name in the search bar.
4. Click on the "Authority Score" section.

Moz will then display an estimate of your brand's authority based on various factors such as backlinks, social signals, and more.

Note: While this is not a direct free Brand Authority Checker, it provides a useful estimate of your brand's authority.