Finding Basis of 5x5 Matrix: A - A^T

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In a solution to an old exam the prof found a basis of a 5x5 matrix by simply subtracting the transpose of A from A aka(A - A^T) and then found the basis for the null for the now much simplified matrix.

Is that a general guideline I can follow? If so it would make my life a lot easier.
 
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Have you posted where you meant to post? That sounds a lot more like Maths than Physics.
 

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