Flipping the labels in a classification problem

Let us say A- we have a binary classifier with labels 1 as healthy and 0 as sick. The precision we got is 100% and the recall is 70%.

Now let us say B-we flip the labels where 0 is healthy and 1 as sick.

Are Precision and recall get flipped in their values if you flip the labels? So in the new case, recall is 100% and precision is 70%?

Or the (70,100) values in the first case belonged to class 1 aka, healthy people and I should calculate the precision and recall for class 0?

My understanding was that we were able to recall 70% of sick people and out of every people who we detected as sick, no person was healthy (precision as 100%). But I am confused now