Finding determinant given determinant of another matrix
1. The problem statement, all variables and given/known data
Let A be a 3 x 3 matrix satisfying the equation [tex]A^{2}[/tex]3A2I=0 where I is the 3x3 identity matrix. Find det(A) given the det(A3)=2 3. The attempt at a solution Well cant find anything like this in my textbook, notes or google. I imagine its a pretty simple matrix property i've overlooked but otherwise i have no clue what to do! Help much appreciated, Ben 
Re: Finding determinant given determinant of another matrix
det(AB) =det(A)*det(B)
So if you factor A^23A you can use det(A3) = 2 
Re: Finding determinant given determinant of another matrix
so
A^2 3A = 2I factors to A(A3)=2I and using property det(AB)=det(A)det(B) det(A)det(A3)=det(2I) so det(A)=det(2I)/det(A3) 
Re: Finding determinant given determinant of another matrix
Yes and you can easily find det(2I).

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