# Regarding transpose of matrix products

1. Feb 6, 2013

### MoreDrinks

Starting out a Lin Alg class - my prof wrote this on the board.

(ABC-1Dt)t = DC-1BtAt

On the right hand side, I get why D is D, why A and B are now both transpose, but why is C still inverse? I know the rule (D-1)t = (Dt)-1, but I do not see how the heck it applies here or what would make the original equality true.

Last edited: Feb 6, 2013
2. Feb 6, 2013

### micromass

Staff Emeritus
It's incorrect, it should be

$$(ABC^{-1}D^t)^t = D (C^t)^{-1} B^t A^t$$

3. Feb 6, 2013

### MoreDrinks

Ugh, I KNEW it was incorrect. He wrote it on the board right before we took a test - he was answering questions - so despite knowing the write answer as you put it, I wrote the wrong thing on the exam. I would have asked, but out the tests came.

This might have something to do with his being an octogenarian. Half hour late to his office hours too and forgets who the heck you are. Son of a...

Thanks for your help. Also, how do you make the script look so nice for writing math?

4. Feb 6, 2013

### Fredrik

Staff Emeritus
5. Feb 6, 2013

### AlephZero

FWIW, some people write $C^{-T}$ instead of $(C^{-1})^T$ or $(C^T)^{-1}$

Maybe you misread $C^{-T}$ as $C^{-1}$.

6. Feb 6, 2013

### MoreDrinks

Could be - wouldn't be in keeping with his writing style though. And it wouldn't be the first mistake we've dealt with.

Thanks a bunch!