I know that the three eigenvalues of the real third order matrix A are -1, 1, 1, and the eigenvector corresponding to eigenvalue -1 is $ (0,1,1)^T$ . I want to find a matrix A that meets the requirements.

A = Array[x, {3, 3}];
FindInstance[(Eigenvalues[A] == {-1, 1, 
     1}) && (A.{{0, 1, 1}}\[Transpose] == -1*{{0, 1, 1}}\[Transpose]) , Flatten[A], Reals]

But the above code returns an empty set. What can I do to find some matrices that meet the constraints?