# Math Help - Determinant

1. ## Determinant

Suppose det A = 3, det B = -2/3, det C = ½
a) find det(A2B-1C)

b) find det(A-1B2C-1)-1

Thankyou in advance for any assistance provided

2. Originally Posted by speckmagoo
Suppose det A = 3, det B = -2/3, det C = ½
a) find det(A2B-1C)

b) find det(A-1B2C-1)-1

Thankyou in advance for any assistance provided
I take it that you mean $\text{det}(A^2B^{-1}C)$ and $\text{det}(A^{-1}B^{2}C^{-1})^{-1}$....

Have you tried using the idea that $\text{det}(A^2B^{-1}C) = \text{det}(A^2)\text{det}(B^{-1})\text{det}(C)$?

Then $\text{det}(A^2) = \text{det}(A)^2$ and $\text{det}(B^{-1}) = \text{det}(B)^{-1}$...

Thankyou very much for your assistance Isomorphism
Yes you are correct in your interpretation of the question. In regards to your suggestion, how would i go about in calculating det A^-1, det A^2, det B^-1, det B^2 and det C^-1

4. det(AB)=det(A)det(B)
det(A^-1)=1/det(A)