I am trying to solve the following problem:
Let $A$ be an $2n$ by $2n$ matrix such that $A^2 = -I_{2n}$. Prove that $A$ is similar to the matrix \begin{equation} \left( \array{0 && -I_n \\ I_n && 0} \right). \end{equation}
I have no idea how to start this problem.