1. ## Please can someone check to see if my answer is right??

So the give eigen value is λ=2.
And the matrix A, what is the basis for each eigenspace?

A=
0 1 1
1 0 1
1 1 0

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My answer that I get after doing (A-2I)x=0 and row reducing it is a general solution and x3 is free.

and my basis is

1
1
1

Can someone tell me if that's right?? please!

2. Hello,

There is another eigenvalue : -1.
In order to help you know if you're on the right way, you can remember that the sum of the eigenvalues equals the trace (the sum of the diagonal elements) of the matrix. And $2 \neq 0$

The eigenspace you found for 2 is correct though