## True or False: Eigenvalues of a Real Matrix Are Real Numbers

## Problem 67

Answer the following questions regarding eigenvalues of a real matrix.

**(a)** True or False. If each entry of an $n \times n$ matrix $A$ is a real number, then the eigenvalues of $A$ are all real numbers.

**(b)** Find the eigenvalues of the matrix

\[B=\begin{bmatrix}

-2 & -1\\

5& 2

\end{bmatrix}.\]

(*The Ohio State University, Linear Algebra Exam*)