I don't think this is a really difficult problem, but there's something I'm missing here.

for 2 matrices, A and B

A=
a 0 0
0 -a 0
0 0 -a

B=
b 0 0
0 0 -ib
0 ib 0

Find three orthonormal vectors which are simultaneous eigenvectors of A and B.

Thanks for any help