Let $s$ and $t$ be two symmetries of $E$ that anticommute, that is, such that $s \circ t + t \circ s = 0$. a) Prove the equalities $t(F_s) = G_s$ and $t(G_s) = F_s$. b) Deduce that $F_s$ and $G_s$ have the same dimension and that $n$ is even.
Let $s$ and $t$ be two symmetries of $E$ that anticommute, that is, such that $s \circ t + t \circ s = 0$.\\
a) Prove the equalities $t(F_s) = G_s$ and $t(G_s) = F_s$.\\
b) Deduce that $F_s$ and $G_s$ have the same dimension and that $n$ is even.