November 13th, 2011, 04:25 AM  #1 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  determinant of BA..... [color=#000000]Let and such that what is the value of ?[/color] 
November 16th, 2011, 10:54 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: determinant of BA..... Assuming there is enough information to solve this, then the precise A and B are not important. So just find A and B that work: in particular Calculate BA with those A and B and find its determinant. 
November 16th, 2011, 11:21 AM  #3 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: determinant of BA.....
2???

November 17th, 2011, 12:49 AM  #4 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: determinant of BA..... [color=#000000]Yes wnvl! The eigenvalues of the matrix AB are 0,1,2, so the characteristic polynomial of AB is so the characteristic polynomial of BA is meaning that det(BA)=2.[/color] 
November 17th, 2011, 12:59 AM  #5  
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: determinant of BA..... Quote:
Didn't know that theorema, but not unlogic.  
November 17th, 2011, 01:20 AM  #6 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: determinant of BA..... [color=#000000]Yes but HallsofIvy made an assumption that might have led to "questionable" conclusions.[/color] 

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