Question

If \( A = \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \), find \( A^{100} \).

• A. \( 100A \)
• B. \( 101A \)
• C. \( A \)
• D. \( 99A \)

Hint:

The power of an identity matrix is always the identity matrix itself.

Answer 1

The Correct Option is C

We are given that \( A = \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \), which is the identity matrix. For any identity matrix, multiplying it by itself any number of times still results in the identity matrix: \[ A^{100} = A \] Thus, the correct answer is option (C).