Let A and B be two invertible matrices of order 3×3. if det ABAT=8 and det⁡AB−1=8, then det⁡BA−1BT is equal to

Let A and B be two invertible matrices of order 3x3. if det ABAT=8 and detAB1=8, then detBA1BT is equal to

  1. A

    1

  2. B

    16

  3. C

    1/16

  4. D

    1/14

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    Solution:

    Here, |A|2|B|=8 …………(i) and  |A||B|=8  ……………….(ii)

    Solving (i) and (ii), we get |A|=4 and |B|=1/2

    Now, detBA1BT=|B|2|A|=1414=116

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