# Transpose of Matrices

• January 30th 2007, 11:11 AM
TreeMoney
Transpose of Matrices
Show that [AB]^t = B^t*A^t........ I know that this is true, I just need proof. I have attempted to figure it out, but I am only able to do it with concrete examples. can someone help me out. TIA!!!!
• January 30th 2007, 11:38 AM
CaptainBlack
Quote:

Originally Posted by TreeMoney
Show that [AB]^t = B^t*A^t........ I know that this is true, I just need proof. I have attempted to figure it out, but I am only able to do it with concrete examples. can someone help me out. TIA!!!!

$(B^tA^t)_{i,j}=\sum_k B^t_{i,k}A^t_{k,j}=\sum_k B_{k,i}A_{j,k}$ $
=\sum_k A_{j,k}B_{k,i}=(AB)_{j,i}=((AB)^t)_{i,j}
$

RonL