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Math Help - multiplication of matrices

  1. #1
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    multiplication of matrices

    Prove if there exists invertible 2x2 matrices A and B such that

    A*B*A^-1*B^-1=2I

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  2. #2
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    this question was recently posted...look in this category.
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  3. #3
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    Quote Originally Posted by appleting View Post
    Prove if there exists invertible 2x2 matrices A and B such that

    A*B*A^-1*B^-1=2I
    If you are asking if there exist invertible matrices A and B such that ABA^{-1}B^{-1} = 2I, then we can easily say there does not. Use determinants.

    However I think you dont know determinants and thats why they have given a 2x2 exercise. So it is the same as saying, AB = 2BA, Now write down the matrices 4 variables and equate the matrices term by term. This will show you that A or B cant be invertible.
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