document.write( "Question 1183381: Let n ∈ N and B is a n × n matrice with real entries and has determinant 1. Show that there exist n × n matrices
\n" ); document.write( "K, A and N such that B = KAN. \n" ); document.write( "
Algebra.Com's Answer #813670 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Surely,  for any  nxn-matrix  B  there are  nxn-matrices  K,  A  and  N  such that   B = KAN.\r
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\n" ); document.write( "\n" ); document.write( "Simply take  A = B,  K = I  (the identity matrix),  N = I.\r
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\n" ); document.write( "\n" ); document.write( "In your post,  you missed some important properties of matrices  A,  B,  K  and  N,  that make the problem  SPECIAL.\r
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\n" ); document.write( "\n" ); document.write( "As it is worded in your post,  the statement is  TRIVIAL.\r
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\n" ); document.write( "\n" ); document.write( "It is valid for any square  nxn-matrix  B,  independently of its determinant.\r
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\n" ); document.write( "\n" ); document.write( "So, twice and thrice check with your source.\r
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\n" ); document.write( "\n" ); document.write( "The term  \"matrice\"  in English is  \"matrix\".\r
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\n" ); document.write( "\n" ); document.write( "Use  \"matrix\"  for single.\r
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\n" ); document.write( "\n" ); document.write( "Use  \"matrices\"  for plural.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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