# determinant problem

• January 27th 2013, 02:53 AM
calc6770
determinant problem
Greetings!

I have a 2 x 2 matrix

3 1
2 0

I will calculate det(A3).

Formula is a11a22-a12a21.

So, 3*0 - 1*2 and that makes det = -2
Thus, det(A3) = (-2)3 = -8

And det(A-3) would be (-2)-3 = -0,125

I think I have calculated correctly. ?
• January 27th 2013, 03:48 AM
abender
Re: determinant problem
In general,
$\det(A^n) = \det(A)^n$.

Edit: So, yes, you are correct, in both instances. Good question.

-Andy
• January 27th 2013, 06:09 AM
calc6770
Re: determinant problem
Thank you, Abender! Very nice to hear that they both are correct!