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#### lemonthree

##### New member

- Apr 11, 2016

- 22

The options are

\(\displaystyle rank(B)+null(B)=n\)

\(\displaystyle tr(ABA^{−1})=tr(B)\)

\(\displaystyle det(AB)=det(A)det(B)\)

I'm thinking that since it's invertible, I would focus on the determinant =/= 0. I believe the first option is out, because null (B) would be 0 which won't be helpful. The second option makes the point that \(\displaystyle AA^{−1}\) is \(\displaystyle I\), so it's suggesting invertibility. So I'm deciding between the second and last option. Does anyone have any tips?

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