# Transposing Matrices

• May 14th 2011, 05:45 PM
rorosingsong
Transposing Matrices
Hi, i'm struggling with this question and really need a push in the right direction... i haven't the faintest idea of what to do here... we haven't learnt about transposing maxtrices yet, I just saw something about it in a text book so I have a vague idea, but I don't really know how to go about proving this:

If A is an m x n matrix with (i,j)- entry $\displaystyle a_{ij}$, let $\displaystyle A^{\dagger}$ be the n x m matrix with (i,j)- entry $\displaystyle a_{ji}$. Show that if the product C= AB is defined, then so is $\displaystyle B^{\dagger}A^{\dagger}$, and that $\displaystyle B^{\dagger}A^{\dagger} = C^{\dagger}$.

rorosingsong
• May 14th 2011, 05:55 PM
pickslides
I think you need to apply the properties of matrix tranposition

If C = AB then C' = (AB)' = A'B'

More here

Transpose - Wikipedia, the free encyclopedia
• May 15th 2011, 12:36 AM
rorosingsong
Thanks pickslides! Appreciate it. =)
• May 15th 2011, 01:07 AM
Prove It
Quote:

Originally Posted by pickslides
I think you need to apply the properties of matrix tranposition

If C = AB then C' = (AB)' = A'B'

More here

Transpose - Wikipedia, the free encyclopedia

Except that $\displaystyle \displaystyle (\mathbf{AB})^T \neq \mathbf{A}^T\mathbf{B}^T$.

However, $\displaystyle \displaystyle (\mathbf{AB})^T = \mathbf{B}^T\mathbf{A}^T$.