Math 6310 • Algebra

Let \(M\) be a matrix with real coefficients such that \(M^2+M+I=0\). Give the possible canonical
forms for \(M\)
\begin{enumerate}
\item[(a.)] Over the real numbers \(\mathbb{R}\) (rational canonical form).
\item[(b.)] Over the complex numbers \(\mathbb{C}\) (Jordan canonical form).
\end{enumerate}