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Math Help - matrix proof 2

  1. #1
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    matrix proof 2

    Can someone please help me with is as i really hate doing matrix proof

    matrix proof 2-untitled.jpg
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  2. #2
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    Quote Originally Posted by nerdo View Post
    Can someone please help me with is as i really hate doing matrix proof

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    for part a, multiply the matrices then take the determinate. that is det(ab). then take det(a), det(b) separately and then find det(a)det(b) then show they are equal.
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  3. #3
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    Quote Originally Posted by GaloisTheory1 View Post
    for part a, multiply the matrices then take the determinate. that is det(ab). then take det(a), det(b) separately and then find det(a)det(b) then show they are equal.

    Oh i get it know, thanks for the help.
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  4. #4
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    For the second part, take the determinant of both sides

    \det(ABA^{-1}B^{-1}) = \det(A)\det(B)\det(A^{-1})\det(B^{-1}) = \det(AA^{-1})\det(BB^{-1}) = 1

    \det(2I_2) = 2

    Therefore no such matrices exist
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  5. #5
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    Quote Originally Posted by SimonM View Post
    For the second part, take the determinant of both sides

    \det(ABA^{-1}B^{-1}) = \det(A)\det(B)\det(A^{-1})\det(B^{-1}) = \det(AA^{-1})\det(BB^{-1}) = 1

    \det(2I_2) = 2

    Therefore no such matrices exist
    thanks i thought it was false, i was trying to figure it out for a while.
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