Question:medium
Let \( |A| = 6 \), where A is a \( 3 \times 3 \) matrix. If \( |\text{adj}(\text{adj}(A^2 \cdot \text{adj}(2A)))| = 2^{m \cdot 3^{n} \), then \( m + n \) is equal to :}
Let \( |A| = 6 \), where A is a \( 3 \times 3 \) matrix. If \( |\text{adj}(\text{adj}(A^2 \cdot \text{adj}(2A)))| = 2^{m \cdot 3^{n} \), then \( m + n \) is equal to :}
Show Hint
Remember the rule for scalars in determinants: $|k \cdot A| = k^n |A|$ where $n$ is the order of the matrix. This is the most common place where students lose marks!
Updated On: Feb 24, 2026
Show Solution
Correct Answer: 62
Solution and Explanation
Was this answer helpful?
0
Top Questions on Vector Algebra
- The value of \( \hat{i} \cdot (\hat{k} \times \hat{j}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{j} \times \hat{i}) \) is _____
- GUJCET - 2026
- Mathematics
- Vector Algebra
- If two vectors \( \vec{a} \) and \( \vec{b} \) are such that \( |\vec{a}| = 2, |\vec{b}| = 3 \) and \( \vec{a} \cdot \vec{b} = 4 \), then \( |\vec{a} - \vec{b}| = \)_____
- GUJCET - 2026
- Mathematics
- Vector Algebra
- Let \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \lambda \hat{j} + 2\hat{k} \), where \( \lambda \in \mathbb{Z} \), be two vectors. Let \( \vec{c} = \vec{a} \times \vec{b} \) and \( \vec{d} \) be a vector of magnitude \(2\) in the \(yz\)-plane. If \( |\vec{c}| = \sqrt{53} \), then the maximum possible value of \( (\vec{c}\cdot\vec{d})^2 \) is equal to
- JEE Main - 2026
- Mathematics
- Vector Algebra
- Let \( \overrightarrow{AB} = 2\hat{i} + 4\hat{j} - 5\hat{k} \) and \( \overrightarrow{AD} = \hat{i} + 2\hat{j} + \lambda \hat{k} \), \( \lambda \in \mathbb{R} \). Let the projection of the vector \( \vec{v} = \hat{i} + \hat{j} + \hat{k} \) on the diagonal \( \overrightarrow{AC} \) of the parallelogram \( ABCD \) be of length one unit. If \( \alpha, \beta \), where \( \alpha>\beta \), be the roots of the equation \( \lambda^2 x^2 - 6\lambda x + 5 = 0 \), then \( 2\alpha - \beta \) is equal to
- JEE Main - 2026
- Mathematics
- Vector Algebra
- Want to practice more? Try solving extra ecology questions todayView All Questions
