How Does Matrix Inversion Affect Diagonal Transformation?

[yeeyee]

Thank you
1. What is the value of the following matrix multiplication




2. $$A^{-1}DA^{T}=?$$
D is diagonal matrix




3. and how to find D to make $$a_i C Z$$


4. $$A^{-1}DA^{T}$$


$$a_i$$ is elements of $$A^{-1}$$
My head really aches, please help

 

[yeeyee]

C is "belongs to" Z, I mean

I can't write a \belongto

 

[HallsofIvy]

You want the components of A^-1 integers? I'm not sure what your question is. If the components of A itself are integers and A has determinant = 1, then the components of A^-1 are integers. D has nothing to do with that- especially since you haven't told us anything about ADA^-1. Is there some condition on that?

Oh, and $a_n \in Z$ is written [ itex ] a_n\in Z[ /itex ], without the spaces, of course.