## xEnOnn 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?

1. JohnnyBreuer

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

2. JohnnyBreuer

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

3. xEnOnn

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.

4. JohnnyBreuer
5. JohnnyBreuer

i can only find proofs using elementary matrices and operations

6. estudier
7. xEnOnn

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