Is there a nice way to show that Det(AB)=Det(A)Det(B) where A and B are n x n matrices over a commutative ring?(adsbygoogle = window.adsbygoogle || []).push({});

I'm hoping there is some analogue to the construction for vector spaces that defines the determinant in a natural way using alternating multilinear mappings...

Otherwise would you just have to bash out the identity using the Leibniz formula for the determinant?

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# Proof that Determinant is Multiplicative for Commutative Rings

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