I need to find the characteristic polynomial, eigenvalues, and eigenvectors or the following matrix.

[1 1]

[1 1]

So far, this is what I have done:

det(Lamda-A) And got

[lamda - 1 -1]

[-1 lamda - 1]

The det of that gives (lamda - 1)(lamda-1) + 1 which is lamda squared - 2 lamda +2

I used the quad formula on that and got 1 plus/minus i

I dont know where to go from here. I think Now i do this:

A-(1+i)I =

[i 1]

[1 i]

i have no clue where to go from there

Please help. THanks