# 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?