i need to find the eigenvalues and vectors of this matrix

[0 1]

[-1 0]

lamda - A gives me this:

[Lamda -1]

[1 Lamda]

Solve the det of this to get lamda squared +1

Only solution is imaginary, i and -i

The matrix of ilamda - A:

[i -1]

[1 i]

Not sure what to do here. Never worked with imaginary numbers in a matrix. Can someone show me how to solve this. Thanks