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Let $A$ be an $n \times n$ real skew-symmetric matrix
  1. The trace of a real skew-symmetric matrix is always equal to $0.$
  2. If $A$ is skew symmetric matrix, then $A^{2}$ is a symmetric matrix.
  3. If $n$ is odd, $A$ is not invertible
  4. If $n$ is even, $A$ is invertible
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A skew symmetric matrix is a square matrix A where $A^{T}$ = -$A$ and also all diagonal entries are zero and a$_{ij}$ $=$ $-a_{ji}$

option A is true since the diagonal entries are zero and trace of matrix equals sum of the diagonal elements

option B is true, refer https://en.wikipedia.org/wiki/Skew-symmetric_matrix#Properties

option C is true and D is false, refer https://en.wikipedia.org/wiki/Skew-symmetric_matrix#Determinant

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