i need help solving this ! most important A)

2. Consider the matrix A=0.531250.131250.06250.131250.1750.481250.731250.13750.618750.1750.46250.13750.7250.33750.150.41250.13750.0751.08750.20.0250.0250.050.0750.85 We will find an approximation of the inverse of A by using a trick similar to what we did in problem 11 . Follow the steps: a) Find a matrix B such that A=I5B. We would love it if B was nilpotent, since in that case we could apply what we did in #1. Sadly B is not nilpotent, but it does have a special property that will allow us to obtain our approximation. b) Use Python to find the eigenvalues of B. You will get some eigenvalues to be complex. This is fine, what matters is the real part of the elgenvalues. You should get that all real parts of the eigenvalues to be less than 1 . [1 c) Why does part b) impply that as n gets bigger Bnv0 ? [1 d) Explain why as n gets bigger, the product A(I5+B+B2++Bn) gets closer and closer to I5. (1) e) Our approximation of A1 is precisely the matrix (I5+B+B2++Bn). Use n=20 to approximate the inverse of A, find this approximation. Check how good (or bad) is our approximation by multiplying A with this approximation of its inverse. Comment on the result. I ] f) Comment on the key points of why this method works. Would it work for any matrix A? Why or why not