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Find the matrix P?

Find the matrix P that multiplies (x, y, z) to give (y, z, x). Find the matrix Q that multiplies (y, z, x) to bring back (x, y, z).
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1 Answer

x goes from 1st to 3rd: put a 1 in 1st column, 3rd row
y goes from 2nd to 1st: put a 1 in 2nd column, 1st row
z goes from 3rd to 2nd: put a 1 in 3rd column, 2nd row.
0's everywhere else.
 
      [0 1 0]
P = [0 0 1]
      [1 0 0]
 
To get back (x,y,z), you just find the inverse,
 
         [0 0 1]
P-1 = [1 0 0]
         [0 1 0]