We say that a matrix $S \in \mathbf{M}_n$ is a symmetry matrix if $S^2 = I_n$. Prove that if $S_1$ and $S_2$ are two symmetry matrices, the product matrix $A = S_1 S_2$ is invertible and similar to its inverse.
We say that a matrix $S \in \mathbf{M}_n$ is a symmetry matrix if $S^2 = I_n$.
Prove that if $S_1$ and $S_2$ are two symmetry matrices, the product matrix $A = S_1 S_2$ is invertible and similar to its inverse.