Check whether the statement below is true or give a counterexample to show it is false.
If $A$ is a $2 \times 2$ matrix with real entries with eigenvalues $\lambda_1$ and $\lambda_2$, then $\lambda_1\cdot\lambda_2$ is always real.
I'm pretty sure I understand it, and that it's true, I'm just not sure how to prove it.