Show that if a $3\times 3$ matrix $A$ represents the reflection about a plane, then $A$ is similar to the matrix $\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & -1 \end{bmatrix}$
This is not homework, just me preparing for a test -- but how can this be solved? I know the definition of similarity, but can't find a way to approach the problem.