Let A, B be two matrices different from identify matrix such that `AB=BA` and `A^(n)-B^(n)` is invertible for some positive integer n. If `A^(n)-B^(n)=A^(n+1)-B^(n+1)=A^(n+1)-B^(n+2)`, then

Options

A. `I-A` is non-singular
B. `I-B` is non-singular
C. `I-A` is singular
D. `I-B` is singular

Explanation

To solve the problem step by step, we start with the given conditions and manipulate the expressions accordingly.

### Step 1: Understand the given conditions
We have two matrices \( A \) and \( B \) such that:
1. \( AB = BA \) (they commute)
2. \( A^n - B^n \) is invertible for some positive integer \( n \)
3. \( A^n - B^n = A^{n+1} - B^{n+1} = A^{n+1} - B^{n+2} \)

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