Question:
If \( A = \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \), find \( A^{100} \).
If \( A = \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \), find \( A^{100} \).
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The power of an identity matrix is always the identity matrix itself.
Updated On: Sep 13, 2025
- \( 100A \)
- \( 101A \)
- \( A \)
- \( 99A \)
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The Correct Option is C
Solution and Explanation
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).
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