The following is a matrix (sorry i am not great at entering the info on here):

2 -1 1
-2 2 0 = B
2 0 2

How would I solve the characteristic equation for B and show that the eigenvalues are 0, 2 and 4?

For each eigenvalue, how would I find a corresponding eigenvector?

Could you please show me how to find the eigenvalues of B^2 + I and (B^2 + 3B - I)^-1 and how would I justify these answers.

And finally what is the eigenvector corresponding to the eigenvalue of largest magnitude for the matrix B^2 + I?