Eigenvalues and Eigenvectors

Question

Here answer is B.

Can anyone explain this? I am confused with option A and B.

Answer 1

Option B is correct.

A + I  is given in question , which gives A = 

Now, it's Eigen Values are   0, -1, -1 . We have to find Eigen Vector for λ =  -1

So, [A - λ I ] X = 0 , which gives 

this gives, from first row ,    x - 2z = 0 => x = 2z

            let , z = t , y = s     =>  x = 2t

so, Eigen Vector is   , Option B (Ans).

Answer 2

ANSWER IS (B)