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  4. If A is any square matrix, then which of the following is skew-symmetric?

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Q. If $A$ is any square matrix, then which of the following is skew-symmetric?

Matrices

Solution:

$ (A - A^T)^T = A^T - (A^T)^T = A^T-A = -(A- A^T)$
Hence, $(A - A^T) $ is skew-symmetric.