The units in are

Thus,

This is called a trivial ring, or the ring where(ii) F(e), where F is a field and e^2=0.

The additive element is the only unit.

Unless the notion F(e) means something else?

(It cannot possibly means a simple extension).

All invertible matrices, that is,(iii) M2(F), where F is a field and M2 is a two-by-two matrix.