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Question

Let A and B be two invertible matrices of order 3×3. If det(ABAT)=8 and det(AB1)=8, then det(BA1BT) is equal to :

A
1
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B
14
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C
16
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D
116
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Solution

The correct option is D 116
det(ABAT)=8|A||B||AT|=8|A|2|B|=8 (1) [|A|=|AT| ]

det(AB1)=8
|A||B1|=8|A||B|=8|A|=8|B| (2)

Put |A| from equation (2) in equation (1), we get
64|B|2|B|=8|B|=12|A|=8|B|=4

Now, det(BA1BT)=|B|1|A||BT|
=|B|2|A|=116

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