Math 6010 • Linear Models

Let \(\mathbf{A}\) be a square symmetric matrix.
\begin{enumerate}

\item
Show that if \(\mathbf{A}^{k}\) is the identity matrix for some \(k \ge 2\) then \(\mathbf{A}^{2}\) is the identity matrix.


\item
Show that if \(\mathbf{A}^{k}\) is the zero matrix for some \(k \ge 2\) then \(\mathbf{A}\) is the zero matrix.

\end{enumerate}