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

Mathematics
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let A =2x2 and B=2x2 and compute the determinants leaving them ad-bc and eh-gf then show that the product of that is similar to the det of the product of AB
if this works on a 2x2 then show that it can used on a matrice of any eelement size so long as its square
But 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.

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Other answers:

http://algebra.math.ust.hk/determinant/05_proof/lecture3.shtml#product
i can only find proofs using elementary matrices and operations
http://www.ams.sunysb.edu/~andant/lectures-ams210-spring2003/04-02-03-addendum.pdf
Thanks everyone. I will read them and come back here again if I have any doubts on it. Thanks! :)

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