Prove this equality: $det(\mathrm I_n-\mathbf A\mathbf B)=2^n$

Question

If $\mathbf A$ and $\mathbf B$ are square matrices ($n$ dimensional) which verifies $\mathbf A\mathbf B=-\mathrm I_n$, then prove that: $$det(\mathrm I_n-\mathbf A\mathbf B)=2^n$$

I'm struggling on this problem, because I can't find a link to $2^n$. So, I need a quick hint.

Answer 1

You look for $\det (2 I_n)$ which's clearly equal to $2^n$.