If `A=[{:(1,0,0),(1,0,1),(0,1,0):}]`, then which is true a. `A^(3)-A^(2)=A-I` b. det. `(A^(100)-I)=0` c. `A^(200)=[(1,0,0),(100,1,0),(100,0,1)]` d. `A^(100)=[(1,1,0),(50,1,0),(50,0,1)]`

Options

A. `A^(3)-A^(2)=A-I`
B. det. `(A^(100)-I)=0`
C. `A^(200)=[(1,0,0),(100,1,0),(100,0,1)]`
D. `A^(100)=[(1,1,0),(50,1,0),(50,0,1)]`

Explanation

To solve the problem, we will analyze the given matrix \( A \) and compute its powers step by step.

Given:
\[
A = \begin{pmatrix}
1 & 0 & 0 \\
1 & 0 & 1 \\
0 & 1 & 0
...