determinants

Steven G

Steven G

Elite Member
Joined
Dec 30, 2014
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Hi,
I am trying to prove that det(AB) = det(A)*det(B) using just the definition of a determinant.
I can not see how to show that equations 1 and 2 are equal.
IMG_0620.jpgIMG_0620.jpg
 
Does anyone have any ideas? The proof should follow from the definition. All Linear Algebra books that I have seen/used walk away from proving this fact stating the proof is too advanced for beginning Linear Algebra students. I just can't understand why this fact can't be proven directly from the definition. Sure it seems like alphabet soup but it should work.
 
Jomo said:
Does anyone have any ideas? The proof should follow from the definition. All Linear Algebra books that I have seen/used walk away from proving this fact stating the proof is too advanced for beginning Linear Algebra students. I just can't understand why this fact can't be proven directly from the definition. Sure it seems like alphabet soup but it should work.
Click to expand...
Is this it? I used Russian. Not sure how to auto-translate a web page.

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