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I have a question about determinants that is probably quite simple. I know that if you have a matrix and you interchange rows, the determinant changes. However, if you cyclically change the rows up or down, still in order, the determinant does not change.

What is the theorem or other rule that governs the difference between the two? Is it a fundamental property of matrices that perhaps I've missed along the way? I've searched through a variety of textbooks and websites, and seen that this is indeed true, but no one has provided an explanation as to why.

Thanks!

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# Determinant Question

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