Question

If A and B are 2x2 matrices, det(A)=-1,det(B)=3, then

det(AB)=

det(-2A)=

det(A^T)=

det(B^-1)=

det(B^4)=

Answer 1

det(AB) = det(A) * det(B) = -3

det(-2A) = (-2)^2 * det(A) = -4

det(A^T) = det(A) = -1

det(B^-1) = 1/det(B) = 1/3

det(B^4) = det(B)^4 = 81