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I'm curious if the following statement is true for all prime numbers n,

[itex]\det_{\mathbb{Z}_n}M = (\det_{\mathbb{R}}M)\mod n[/itex]

where [itex]\det_F M[/itex] is the determinant of M over the field F.

Thanks.

James

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# Determinant of a matrix over the integers mod n

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