Question

If \(A=\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\), then \(A^{100}\) is

• A. \(2^{100}A\)
• B. \(2^{99}A\)
• C. \(2^{101}A\)
• D. None of the above

Hint:

Idempotent-like matrices simplify high powers easily.

Answer 1

The Correct Option is B

Step 1: \[ A^2=2A \]
Step 2: \[ A^n=2^{n-1}A \Rightarrow A^{100}=2^{99}A \]