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let A and B two invertible matrices of order $3 X 3$ . If det $(A B A^{T}) = 8 a n d$ det $(A B^{- 1}) = 8,$ then det $(B A^{- 1} B^{T})$ is

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Correct option is C

We have |A||B|AT=8 and |A|1B=8 ∵B-1=1B|A|2|B|=8→ (1) |A|=8|B|→(2) ∵AT=A (1) ⇒64|B|3=8 ⇒|B|=12 and |A|=4∴BA-1BT=|B|=1|A||B|T=121412=116

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let A and B two invertible matrices of order 3X3. If det ABAT=8 and det AB-1=8, then det BA−1BT is

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free study material

let A and B two invertible matrices of order $3 X 3$ . If det $(A B A^{T}) = 8 a n d$ det $(A B^{- 1}) = 8,$ then det $(B A^{- 1} B^{T})$ is