What's the default password of mariadb on fedora?

I had the same problem. It's true the password is empty, but even so the error message is shown. The solution is just using "sudo" so

$ sudo mysql

will open the mysql tool

For securing the database, you should use sudo again.

$ sudo mysql_secure_installation

From https://mariadb.com/kb/en/mysql_secure_installation/ :

In order to log into MariaDB to secure it, we'll need the current password for the root user. If you've just installed MariaDB, and you haven't set the root password yet, the password will be blank, so you should just press enter here.

the password will be blank

I think that's your answer.

mariadb uses by defaults UNIX_SOCKET plugin to authenticate user root. https://mariadb.com/kb/en/mariadb/unix_socket-authentication-plugin/

"Because he has identified himself to the operating system, he does not need to do it again for the database"

so you need to login as the root user on unix to login as root in mysql/mariadb:

sudo mysql

if you want to login with root from your normal unix user, you can disable the authentication plugin for root.

Beforehand you can set the root password with mysql_secure_installation (default password is blank), then to let every user authenticate as root login with:

shell$ sudo mysql -u root
[mysql] use mysql;
[mysql] update user set plugin='' where User='root';
[mysql] flush privileges;
[mysql] \q