We say that a matrix $S \in \mathbf{M}_n$ is a symmetry matrix if $S^2 = I_n$. If a matrix $A$ is a product of two symmetry matrices, is the same true for every matrix similar to $A$?
We say that a matrix $S \in \mathbf{M}_n$ is a symmetry matrix if $S^2 = I_n$.
If a matrix $A$ is a product of two symmetry matrices, is the same true for every matrix similar to $A$?