Describe how $scope inheritance works in nested controllers.

In AngularJS, $scope inheritance works in nested controllers by establishing a hierarchy. Child controllers inherit from their parent controllers, creating a chain of scopes. This means that the child controller can access properties and methods defined in its parent controller's $scope. However, changes made in the child controller's $scope do not affect the parent controller's $scope. Understanding $scope inheritance is crucial for managing data flow and communication between nested controllers in AngularJS applications.