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Let A and B be two invertible matrices o...

Let A and B be two invertible matrices of order `3 xx 3`. If `"det"(ABA^(T)) =8 " and det"(AB^(-1)) =8, " then det"(BA^(-1)B^(T))` is equal to

A

1

B

`(1)/(4)`

C

`(1)/(16)`

D

16

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( \text{det}(BA^{-1}B^T) \) given the conditions: 1. \( \text{det}(ABA^T) = 8 \) 2. \( \text{det}(AB^{-1}) = 8 \) ### Step-by-Step Solution: **Step 1: Use the properties of determinants.** ...
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