I need to find a change of base for Pc<b and Pb<c where:

b=1,1+x,x+x^2

c=1+x,x+x^2,1+x^2

A lot of steps here:

I got:

Pb<c =:

1 0 1

1 1 0

0 1 1

To get Pc<b I used a theorem that Pc<b=(Pb<c)^-1 thus Pc<b:=

1/2 1/2 -1/2

-1/2 1/2 1/2

1/2 -1/2 1/2

Ia this right?

Why I doubt this is that the latter matrix seemed way to wasy compared to the steos involved to get the Pb<c matrix.