Question

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

Answer 1

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

Answer 2

if this works on a 2x2 then show that it can used on a matrice of any eelement size so long as its square

Answer 3

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.

Answer 4

http://algebra.math.ust.hk/determinant/05_proof/lecture3.shtml#product

Answer 5

i can only find proofs using elementary matrices and operations

Answer 6

http://www.ams.sunysb.edu/~andant/lectures-ams210-spring2003/04-02-03-addendum.pdf

Answer 7

Thanks everyone. I will read them and come back here again if I have any doubts on it. Thanks! :)