Yes, you are getting the correct answers for a) and b).

[shiri]

Let A, B and C be 3x3 invertible matrices where det(A)=4 , det(B)=4 and det(C) is some non-zero scalar.

a) det [(C^T)(A^-1)(B^2)(C^-1)]

b) det [-2(A^2)^T(C^2)(B^-1)(C^-1)^2]


a)
What I got is:

det [(A^-1)(B^2)(C^T)(C^-1)]

= det [(A^-1)(B^2)(C)(C^-1)]

= det [(A^-1)(B^2)]

= [1/det(A)]*[det(B)]^2

= (1/4)*(4)^2

= 16/4

= 4


b)
What I got is:

det [-2(A^2)^T(B^-1)(C^2)(C^-1)^2]

= (-2)^3 det [(A^2)^T(B^-1)(C^2)(C^-2)]

= -8 det [(A^2)(B^-1)]

= -8 [det(A)]^2*[1/det(B)]

= -8 (4)^2*(1/4)

= -8 (16)*(1/4)

= -8*4

= -32


Can anyone please tell me, am I getting the right answers for a) and b)?

 

[rock.freak667]

They look correct to me

 

[tiny-tim]

Me too.

… what's worrying you about them?​