If A is a matrix of order n such that `A^(T)A=I` and X is any matric such that `X=(A+I)^(-1) (A-I)`, then show that X is skew symmetric matrix.

Explanation

To show that the matrix \( X = (A + I)^{-1}(A - I) \) is skew-symmetric, we need to demonstrate that \( X^T = -X \).

### Step-by-Step Solution:

1. **Start with the definition of \( X \)**:
\[ X = (A + I)^{-1}(A - I) \]
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