Reflection across a plane

#linear_algebra

Let $a, b \in R$ and $T : R^{3} \to R^{3}$ be the linear transformation which is reflection across the plane $z = a x + b y$ .

Find the eigenvalues of $T$ and for each find a basis for the corresponding eigenspace.
Is $T$ diagonalizable? Justify.
What is the characteristic polynomial of $T$ ?
What is the minimal polynomial of $T$ ?

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Let $a,b\in {\bf R}$ and $T:{\bf R}^3\to {\bf R}^3$ be the linear transformation which is reflection across the plane $z=ax+by$.
\begin{enumerate}[label=(\alph*)]
	\item Find the eigenvalues of $T$ and for each find a basis for the corresponding eigenspace.
	\item Is $T$ diagonalizable? Justify.
	\item What is the characteristic polynomial of $T$?
	\item What is the minimal polynomial of $T$?
\end{enumerate}