## An Example of a Real Matrix that Does Not Have Real Eigenvalues

## Problem 596

Let

\[A=\begin{bmatrix}

a & b\\

-b& a

\end{bmatrix}\]
be a $2\times 2$ matrix, where $a, b$ are real numbers.

Suppose that $b\neq 0$.

Prove that the matrix $A$ does not have real eigenvalues.

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