# Representation of a reflection about a plane in $\mathbb{R}^3$

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.

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