Final answer:
The determinant of AB is 24. The determinant of -2A is -48. The determinant of B^-1 is -1/8.
Step-by-step explanation:
To find the determinant of the product of matrices A and B (AB), you can use the property det(AB) = det(A) * det(B). So, det(AB) = det(A) * det(B) = (-3) * (-8) = 24.
To find the determinant of -2A, we can use the property det(kA) = k^n * det(A), where k is a scalar and n is the size of the matrix. Since A is a 4x4 matrix, det(-2A) = (-2)^4 * det(A) = 16 * (-3) = -48.
To find the determinant of the inverse of matrix B (B^-1), we use the property det(B^-1) = 1 / det(B). So, det(B^-1) = 1 / det(B) = 1 / (-8) = -1/8.