matrix – How to find some matrices that satisfy the constraints


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?