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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?
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?
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?