So the eigenvalues of a are 3,3,0.

Because the eigenvalues of B are 1 and 1, 0, A and B are not similar (if they are similar, the eigenvalues are the same).

And a is a real symmetric matrix, so the orthogonality of a is similar to diag (3,3,0), so it is reduced to B=diag( 1, 1, 0).

(The necessary and sufficient condition of the contract is that the positive and negative inertia indexes are the same)

So (b) is correct.