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June 3rd, 2014, 11:24 AM   #1
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Determinant proof for 3 by 3 matrices

To get the determinant of 3 by 3 matrices we're told to just reduce the 3 by 3 matrix into three 2 by 2s by essentially taking 3 terms in the matrix and eliminating their column and row and then multiplying those terms by their respective 2 by 2 sub-matrices. I'm able to use the method, but I don't like blindly applying methods like this without having at least some intuition of why they work. I've looked at a geometric proof for why the determinant of a 2 by 2 matrix is ad-bc and it makes sense, but I havent been able to find a proof for the method that I described above. Why in the world does that work?
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June 4th, 2014, 08:18 PM   #2
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It is possible by multiplication only there is not any other option to change 3 by 3 matrix in 2 by 2.
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