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If A is a symmetric matrix, B is a skew-...

If A is a symmetric matrix, B is a skew-symmetric matrix, `A+B` is nonsingular and `C=(A+B)^(-1) (A-B)`, then prove that
(i) `C^(T) (A+B) C=A+B` (ii) `C^(T) (A-B)C=A-B`
(iii) `C^(T)AC=A`

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