Discrete Math Proof: Solving Homework Equations

[Bashyboy]

Homework Statement

I attached the problem as a file.

Homework Equations

The Attempt at a Solution

I get stuck on how to properly represent the summation. How does k find it's way as one of the sub-scripts?

 

[HallsofIvy]

Your post makes no sense and there is no attachment.

 

[Bashyboy]

I am so sorry, I'll fix that.

 

[HallsofIvy]

Okay, you have B^TA^T. Now, what is (AB)^T?

 

[Bashyboy]

So,

$AB = \sum_k a_{ki}b_{jk}$

$(AB)^t = \sum_k a_{ki} b_{jk} = \sum_k b_{jk} a_{ki} = B^tA^t$

Does that look correct?