prove that the following matrix [[-2/3 1/3 2/3] [2/3 2/3 1/3] [1/3 -2/3 2/3]] is orthogonal

we use * for dot product 
v1*v1=4/9+1/9+4/9=1
v1*v2=-4/9+2/9+2/9=0
v1*v3=-2/9-2/9+4/9=0 

v2*v1=v1*v2=0
v2*v2=4/9+4/9+1/9=1
v2*v3=2/9-4/9+2/9=0 

v3*v1=v1*v3=0
v3*v2=v2*v3=0
v3*v3=1/9+4/9+4/9=1 


:)