Let a matrix of order n have n eigenvalues 0,1,2,..., n-1, and B ~ A, and find det (I + b)

Let a matrix of order n have n eigenvalues 0,1,2,..., n-1, and B ~ A, and find det (I + b)

1) A is similar to B, so what is the eigenvalue of B?
2) What is the relationship between the eigenvalues of I + B and B?
3) What is the relationship between eigenvalues and determinants?
If you answer the above three questions, you will get it