Find the matrix P?

Question

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).

Answer 1

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]