Question:medium
If $A$ is a square matrix of order $n$ such that $|\text{adj}(\text{adj} A)|=|A|^{25}$, then $n$ is equal to
If $A$ is a square matrix of order $n$ such that $|\text{adj}(\text{adj} A)|=|A|^{25}$, then $n$ is equal to
Show Hint
Logic Tip: Memorize the adjoint determinant hierarchy for a matrix $A$ of order $n$:
1. $|\text{adj} A| = |A|^{n-1}$
2. $|\text{adj}(\text{adj} A)| = |A|^{(n-1)^2}$
3. $\text{adj}(\text{adj} A) = |A|^{n-2} A$
Updated On: Apr 27, 2026
- 6
- 4
- 5
- 3
- 7
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Determinants
- If \( f(x) \) is differentiable at \( x = 1 \) and \[ \lim_{h \to 0} \frac{1}{h} f(1 + h) = 5, \] then \( f'(1) \) is equal to:
- MHT CET - 2024
- Mathematics
- Determinants
- If \( A = \begin{bmatrix} 2 & 1
3 & 4 \end{bmatrix} \), then the determinant of matrix \( A \) is:- MHT CET - 2025
- Mathematics
- Determinants
- Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]- MHT CET - 2025
- Mathematics
- Determinants
- Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
- MHT CET - 2025
- Mathematics
- Determinants
- Want to practice more? Try solving extra ecology questions todayView All Questions
