[Gate IN 2016- Set A] Linear algebra,Eigen values

Question

If we solve this we will get total 4 eigen vectors,but as we know that this is of 2 degree matrix so only 2 will exist.So can i say that from these four pairs by using nay 2 ,i can derive the other?If yes,then how?

Comments

how option 'c' could be answer??....in second pair of eigenvector [0 1], it is not possible because here x=0 and since either x or y is linearly dependent on other then other should also be 0...

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what will be its eigen values and vector please explain

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here , there will be two eigen vectors ({1,-j} corresponding to eigen value i  and {j,-1} corresponding value -i).

Answer 1

The answer is A

,Since the eigen value is j, and -j finding the corresponding eigen vector, which gives  {1 -i} and {i,-1} respectively