What does it mean when $\mathrm{det}(I-Q^2)=0$ where $Q$ is Toeplitz?

Question

Assume $Q$ is a general Toeplitz matrix. Under what conditions can we make sure $$\mathrm{det}(I-Q^2)\neq 0?$$

Let's denote the determinant by $|\cdot|$. We can show that $$|I-Q^2| = |I-Q||I+Q|\neq 0 .$$ Thus,
$$|I-Q|\neq 0 \text{ and }|I+Q|\neq 0 .$$ What does it mean?