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Math Help - Is the Iverse of Skewed-Symmetric, Invertible Matrix A also Skewed-Symmetric

  1. #1
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    Is the Iverse of Skewed-Symmetric, Invertible Matrix A also Skewed-Symmetric

    A is invertible, skewed symmetric
    Transpose(A) = -(A)

    Is Inverse(A) skewed symmetric?
    Does Transpose(Inverse(A)) = -Inverse(A)?
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  2. #2
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    Re: Is the Iverse of Skewed-Symmetric, Invertible Matrix A also Skewed-Symmetric

    Let A be an nxn matrix. Assume that A is skew-symmetric. Then A^T = -A. The question is whether A^-1 is skew-symmetic. The answer is yes simply because of the fact that (A^-1)^T = (A^T)^-1. Note that

    (A^-1)^T = (A^T)^-1 = (-A)^-1 = -A^-1
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