Given $\det(A)$ and $\det(B)$, is my calculation of $\det(-2B^T B A)$ correct?

Question

Suppose $A$ and $B$ are $3 \times 3$ matrices with $\det(A) = -2$ and $\det(B) = -1$.

What is the determinant of $C = -2 B^T B A$?

I know that $$\det(A^T) = \det(A) \qquad \det(AB) = \det(A) \det(B)$$ so I got $$\det(C) = -2(-1)(-1)(-2) = 4$$ Is this correct?

Answer 1

No. Notice that for a matrix $A\in\mathcal M_n(\Bbb F)$ and $\lambda\in\Bbb F$ we have

$$\det(\lambda A)=\lambda^n\det(A)$$