 Solution

ID: past-exam-of-the-algebra-1-and-differential-equations-1-course-of-the-university-of-oxford/2015/1/b/iii/solution

No. On any nonzero vector space over a field of characteristic two, take

E = F = I

E + F = 0 is a linear projection, EF = FE = I \neq = 0.

The correct condition from part (i) in this characteristic is

EF = FE

, because minus and plus coincide. Vanishing of both products remains sufficient, but is no longer necessary.

 New to topics? Read the docs here!