I found the following question:
Let $V$ be a finite dimensional inner product space over $C$ and let $T$ in $A(V)$ be unitary transformation. Prove that if $U$ is a subset of $V$ and it is $T$-Invariant then also the orthogonal complement of $U$ is $T$-Invariant.
What does the set $A(V)$ means?
I tried to do the following: Let $x$ be in the orthogonal complement of $U$, we need to show that for every y in $U$ $(T(x),y) = 0$. If $T = T^*$ then $(T(x),y) = (x,T^*(y)) = (x,T(y)) = 0$ but in this case $T^* = T-1$ so $(T(x),y) = (x,T-1(y))$ but I don't know how to continue from here.