i need to prove the following:
this is what i've tried so far:
iff A is invertible.
since A is invertible, it can be presented as a product of elementary transformations:
now, since E is either , , or its determinant is 1, -1 or respectivly, then:
my problem is with my last sentence: i'm kinda using what i need to prove in my proof...
i can really use a guidance here.
plus, how can i prove the other direction? ( )
thanks in advanced!