Question:
If \(A=\begin{bmatrix}1&0 \\ 0&1\end{bmatrix}\), then the value of \(A^{25}\) is
If \(A=\begin{bmatrix}1&0 \\ 0&1\end{bmatrix}\), then the value of \(A^{25}\) is
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Raising the identity to any power gives the identity back: \(I^n=I\).
Updated On: Oct 17, 2025
- \(25A\)
- \(24A\)
- \(2A\)
- \(A\)
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The Correct Option is D
Solution and Explanation
The given matrix is the identity \(I_2\). Identity is the multiplicative neutral element:
\[
I_2^n=I_2\text{for any positive integer }n.
\]
Therefore,
\[
A^{25}=I_2^{25}=I_2=A.
\]
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