(b) In this part let's calculate A- using R. Let -6 -2 A = 3 - 1 -3 1 3 -1 i. (3 points) Write an R code calculate the A-. Note your answer should include your R code and the output showing your calculated A-. ii. (3 points) Extend your R code to multiply the matrices calculating AA-A.7. (Generalized Inverse of a matrix) In statistics, we sometimes encounter matrices that are not invertible. In such situ- ations. we often use the generalized inverse, which has properties similar to that of the inverse. A generalized inverse of any m x n matrix A is any n x m matrix A- such that AA- A = A. Note: A generalized inverse is not unique. If A is a non-singular square matrix, then A- = A-. This can also be calculated for non-square matrices. (a) In this part we will investigate some basic properties of A-. i. (4 points) Prove that AA- and A-A are idempotent matrices. ii. (3 points) Prove that rank(A) = rank(AA-). Hint: For conformable matrices rank(AB)