Therefore, if a stress element is subjected to plane stress, then the out-of-plane face (i.e., the $z$ face in this illustration) is a principal plane and the normal stress ${\sigma }_z$ acting on the $z$ face is a principal stress.

If ${\sigma }_z$ is a principal stress, what is its magnitude?

Since the element is subjected to plane stress, all stresses in the out-of-plane direction must be zero. Therefore, ${\sigma }_z=0$.