(one's) word is law(redirected from their word is law)
(one's) word is law
One has the ultimate authority; you must do what one says. You better do it, or you know what'll happen. Mom's word is law. I don't care what your supervisor said. I'm the boss here, so my word is law.
someone's word is law
If someone's word is law in an organization or group, everyone has to obey them. Inside the firm, Potter's word was law. His father was the kind of parent who saw no reason to discuss anything with his son; his word was law. Note: This expression is often used to suggest that this kind of behaviour is unreasonable.