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 3 years ago
How can I prove that it is true that \[det(AB)=det(A) \times det(B)\] where A and B are square matrices?
 3 years ago
How can I prove that it is true that \[det(AB)=det(A) \times det(B)\] where A and B are square matrices?

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JohnnyBreuer
 3 years ago
Best ResponseYou've already chosen the best response.0let A =2x2 and B=2x2 and compute the determinants leaving them adbc and ehgf then show that the product of that is similar to the det of the product of AB

JohnnyBreuer
 3 years ago
Best ResponseYou've already chosen the best response.0if this works on a 2x2 then show that it can used on a matrice of any eelement size so long as its square

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.0But is there a more proper and concrete proof instead of using the 2x2 matrix formula for determinants? I know that this is true for all matrices of order n. But I wanted to prove it in a more concrete manner.

JohnnyBreuer
 3 years ago
Best ResponseYou've already chosen the best response.0http://algebra.math.ust.hk/determinant/05_proof/lecture3.shtml#product

JohnnyBreuer
 3 years ago
Best ResponseYou've already chosen the best response.0i can only find proofs using elementary matrices and operations

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1http://www.ams.sunysb.edu/~andant/lecturesams210spring2003/040203addendum.pdf

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks everyone. I will read them and come back here again if I have any doubts on it. Thanks! :)
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