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
Show Hint
Raising the identity to any power gives the identity back: \(I^n=I\).
Updated On: Oct 17, 2025
- \(25A\)
- \(24A\)
- \(2A\)
- \(A\)
Hide Solution
Verified By Collegedunia
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,
\[
A^{25}=I_2^{25}=I_2=A.
\]
Was this answer helpful?
0
0
Top Questions on Matrix Operations
- Let $ A = [a_{ij}] $ be a $3 \times 3 $ matrix such that: $$ A = \begin{bmatrix} 0 & 0 & 4 \\ 1 & 0 & 0 \\ 0 & 1 & 3 \\ \end{bmatrix}, A^{-1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 3 & 0 \\ 2 & 1 & 0 \end{bmatrix}. $$ Then $ a_{23} $ equals:
- JEE Main - 2025
- Mathematics
- Matrix Operations
- Match List-I with List-II.\[\begin{array}{|c|c|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}, \; \Delta \text{ is} & (I) \; 0 \\ \hline (B) \; \text{If } A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}, \; \Delta \text{ is} & (II) \; 1 \\ \hline (C) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}, \; |A^{-1}| \text{ is} & (III) \; -2 \\ \hline (D) \; \text{If } A = \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}, \; a \text{ is} & (IV) \; 2 \\ \hline \end{array}\]
- CUET (PG) - 2025
- Computer Science
- Matrix Operations
- If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).
- KEAM - 2025
- Mathematics
- Matrix Operations
- Multiply the matrices: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \]
- Bihar Board XII - 2025
- Mathematics
- Matrix Operations
Find the product of the matrices: \[ \left[ \begin{matrix} 6 & 5 \end{matrix} \right] \left[ \begin{matrix} -1 \\ 1 \end{matrix} \right] \]
- Bihar Board XII - 2025
- Mathematics
- Matrix Operations
View More Questions
Questions Asked in Bihar Board XII exam
- Explain the characteristics of a good brand.
- Bihar Board XII - 2025
- Entrepreneurship: Concept, Functions and Need
- Explain the different kinds of capital.
- Bihar Board XII - 2025
- Business Strategy
- What are the responsibilities of an entrepreneur towards society? Explain.
- Bihar Board XII - 2025
- Entrepreneurship: Concept, Functions and Need
- Define planning and mention its features.
- State any two objectives of project report.
- Bihar Board XII - 2025
- Project Planning
View More Questions