Error 1628: Acess denied for user 'root'@'localhost' (Install mysql)

ERROR 1698 (28000): Access denied for user 'root'@'localhost'

# ERROR 1698 (28000): Access denied for user 'root'@'localhost', change password mysql.

$ sudo mysql -u root # I had to use "sudo" since is new installation

mysql> USE mysql;
mysql> SELECT User, Host, plugin FROM mysql.user;

+------------------+-----------------------+
| User             | plugin                |
+------------------+-----------------------+
| root             | auth_socket           |
| mysql.sys        | mysql_native_password |
| debian-sys-maint | mysql_native_password |
+------------------+-----------------------+

mysql> UPDATE user SET plugin='mysql_native_password' WHERE User='root';
mysql> FLUSH PRIVILEGES;
mysql> exit;

$ service mysql restart

$ sudo mysql -u root # I had to use "sudo" since is new installation

mysql> USE mysql;
mysql> ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'new-password';
mysql> FLUSH PRIVILEGES;
mysql> exit;

$ service mysql restart

##

root pass: *81F5E21E35407D884A6CD4A731AEBFB6AF209E1B