Let $(E , \omega)$ be a symplectic vector space of dimension $n = 2m$. Let $a \in E$ be a non-zero vector and let $\lambda$ and $\mu$ be real numbers. The symplectic transvections are defined by $\tau _ { a } ^ { \lambda } ( x ) = x + \lambda \omega ( a , x ) a$. Show that $\tau _ { a } ^ { \mu } \circ \tau _ { a } ^ { \lambda } = \tau _ { a } ^ { \lambda + \mu }$.