What does it mean for det($A^2-\lambda I_n)=0$ to have a zero solution, assuming $A$ is an invertible matrix?

Question

If it means that $\lambda$ must be zero, then I think the statement is incorrect as det($A)\ne 0$. Could someone clarify the meaning?

Answer 1

If it has a zero solution then $\det A^2 = 0$.

But $\det A^2 = \det A\ \det A \ne 0.$