Does flipping binary class labels impact performance metrics?

I am working on a classification problem with 0 and 1 class labels. I am wondering if I flip the class labels (i.e if I label all the formerly 0 classes as 1 and all the formerly 1 classes as 0) how machine learning performance metrics would change, if it all.

The metrics I am considering are: weighted F1 score, accuracy, balanced accuracy, AUC, precision, and recall.

My intuition is that all metrics would stay the same except precision and recall, which would be flipped (i.e. the precision and recall relative to the former 0 class would be the precision and recall for the new 1 class, etc). Is this accurate?