Get matrix A from a series of elementary matrices

Tom Salazar
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1. Get A from its inverse
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3. I believe it has something to do with the theorem that states: E1E2E3...EkA=I
 
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There's an identity that says that ##(MN)^{-1} = N^{-1} M^{-1}## that would be useful here. You should also consult your text about how to determine the inverse of an individual matrix. They probably discuss the method that uses the matrix of cofactors.
 
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fzero said:
There's an identity that says that ##(MN)^{-1} = N^{-1} M^{-1}## that would be useful here. You should also consult your text about how to determine the inverse of an individual matrix. They probably discuss the method that uses the matrix of cofactors.

Thank you very much!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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