Hello I'm having some issues with this current problem and I'm hoping that someone can help.

The problem states: Given A is an n x n invertible matrix such that lamda is equal to 1 is not an eigenvalue, I is the identity matrix, (A^1) is the inverse matrix of A. Explain why

a) (I-A^-1) is invertible

b) (A^-1)(I-A^-1) = (A-I)^-1

c) ((I-A^-1)^-1)(A^-1) = (A-I)^-1