Transpose of Matrices

**TreeMoney** · January 30th 2007, 11:11 AM

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!!!!

**CaptainBlack** · January 30th 2007, 11:38 AM

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!!!!

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

RonL

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