How to write or show statements for a matrix of order 2 or more

Question

Let $A$ be an $n \times n$ orthogonal matrix where $n$ is even, $|A|=-1$. Show that $|I-A|=0$.

I can prove this statement for a matrix of $n=2$, I can slog and also provide a proof for $n=4$, but how can I generalize the idea for a proof?