If S is a real skew-symmetric matrix, then how can you show that S-I is non-singular?

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If S is a real skew-symmetric matrix, the show that I-S is non-singular and matrix A=(I+S)(I-S)^-... If S is a real skew-symmetric matrix, the show that I-S is non-singular and matrix A=(I+S)(I-S)^-...
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