For some information I've get error after changing password:
Access denied for user 'root'@'localhost' (using password: NO)
Access denied for user 'root'@'localhost' (using password: YES)
In both cases there was error.
But the thing is after that I've tried it with
mysql -uroot -ppassword
instead of
mysql -u root -p password
-> with spaces between -uroot and -ppassword so maybe if someone get trouble can try this way.