Solution
= Solution
\b[No.] On any nonzero <vector space> over a <field> of <characteristic> two, take $E=F=I$. Both are <linear projections>, and
$$
\boxed{E+F=0\text{ is a linear projection},\qquad EF=FE=I\ne0.}
$$
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.