Determinant of 5x5 matrices

Question

Let A and B be 5x5 matrices with det(-3A)=4 and det(B^-1)=2. Find the det(A), det(B) and det(AB).

My answer : det(A)=-12 , det(B)=1/2 and det(AB)=-6. Wish to check my answer, thank you.

Answer 1

$\det(-3A) = (-3)^5 \det(A)$. Because in general: if $A$ is an $n \times n$ matrix, we have $\det(xA) = x^n \det(A)$. Thus,

$$\det(A) = \frac{-4}{3^5}$$

Your $\det(B)$ is correct.

Finally, $\det(AB) = \det(A) \times \det(B)$.