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Need help to find my mistake in a simple proof of a matrix algebra proposition. 
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#1
Sep2508, 01:20 PM

P: 7

1. The problem statement, all variables and given/known data
Is the following true for matrices? Hypotesis: AB = AC A != 0(zero matrix) Thesis: B=C 3. The attempt at a solution AB = AC AB  AC = 0(zero matrix) AB  AC = A(BC) // using the following property: A(B+C) = AB + AC iff A is mn matrix and BC are np matrices A(BC) = 0 <=> B=C because A != 0 QED There is something wrong because there are matrices where AB = AC and B != C. Where is my mistake? 


#2
Sep2508, 01:32 PM

Sci Advisor
HW Helper
Thanks
P: 25,246

There are matrices where AB=0 and neither A nor B are zero. You can't say A(BC)=0 implies A=0 or (BC)=0 like you can with real numbers.



#3
Sep2508, 01:45 PM

P: 7

ok, thanks



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