If A, B are two n x n non-singular matrices, then

If A, B are two n x n non-singular matrices, then

  1. A

    AB is non-singular

  2. B

    AB is singular

  3. C

    (AB)1=A1B1

  4. D

    (AB)1 does not exist

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    Solution:

    We have,

    |AB|=|A||B|0             [|A|0,|B|0]

    Therefore, AB is a non-singular matrix.

    Consequently, (AB)1 exists and  (AB)1=B1 A1

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