# Thread: A matrix that permutates row vectors to column vectors

1. ## A matrix that permutates row vectors to column vectors

The question is, which 3X3 matrix permutates (x,y,z) to (z,x,y). In other words, you can write the vectors once as a row and once as a column vector.

2. Check this out.
$\left( {\begin{array}{ccc} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ \end{array} } \right)$

Does it work? WHY?

3. Yeah, it works. Was trying to think why but couldn't find an answer. The only property I could think of now is that it has zeros filled in the main diagonal. I would appreciate if you explain. Thanks in advance.

4. Well you take a close look at it!
The first row 'picks up' the third element.
The second row 'picks up' the first element.
The third row 'picks up' the second element.

5. Originally Posted by Plato
Well you take a close look at it!
The first row 'picks up' the third element.
The second row 'picks up' the first element.
The third row 'picks up' the second element.
Oh OK I get it now. Thanks.