Answer
-1152
Work Step by Step
If A and B are $4 \times 4$ matrices, then:
$\det(AB)=\det(A).\det(B)$
Also $\det (A^T)=\det(A)$
and if $\det(A) \ne 0 $ then $\det(A^{-1})=\frac{1}{\det(A)}$
Hence here,
$\det((−A)^3(2B^2))=\det((−A)^3 \det(2B^2))=(\det(−A))^3(2^4 \det B^2))=(-2)^3.(16.(3))^2 =-1152$
