# Finding determinant given determinant of another matrix

1. ### bojo

5
1. The problem statement, all variables and given/known data

Let A be a 3 x 3 matrix satisfying the equation $$A^{2}$$-3A-2I=0 where I is the 3x3 identity matrix. Find det(A) given the det(A-3)=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

2. ### rock.freak667

6,221
det(AB) =det(A)*det(B)

So if you factor A^2-3A you can use det(A-3) = 2

3. ### bojo

5
so

A^2 -3A = 2I factors to

A(A-3)=2I

and using property det(AB)=det(A)det(B)

det(A)det(A-3)=det(2I) so det(A)=det(2I)/det(A-3)

4. ### rock.freak667

6,221
Yes and you can easily find det(2I).

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