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Math Help - Matrix identities and determinants

  1. #1
    Newbie SuumEorum's Avatar
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    Matrix identities and determinants

    Hey there, I just wanted to confirm something, if AB=I where A and B are square matrices and I the identity matrix, can we then say that |A||B|=|I|? Thanks a lot .
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    Quote Originally Posted by SuumEorum View Post
    Hey there, I just wanted to confirm something, if AB=I where A and B are square matrices and I the identity matrix, can we then say that |A||B|=|I|? Thanks a lot .
    From what I can tell, yes. For instance:

    1 2
    3 1

    has an inverse of
    -1/5 2/5
    3/5 -1/5

    The determinant of the first matrix is:
    -5 ((1x1)-(2X3))
    And the second is:
    -1/5.

    By multiplying the two, you get 1, which is det(I).
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  3. #3
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    You can do that with any matrices (not just the identity) because

    det(AB)=det(A)det(B)
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  4. #4
    Newbie SuumEorum's Avatar
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    Aah I see, thanks
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  5. #5
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    Quote Originally Posted by whipflip15 View Post
    You can do that with any matrices (not just the identity) because

    det(AB)=det(A)det(B)
    I was going to put that in, but I wasn't 100% sure it was relevant.
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