Class CBSE Class 12 Mathematics Matrices and Determinants Q #850
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If |A|=2, where A is a 2\times2 matrix, then |4A^{-1}| equals :
(A) 4
(B) 2
(C) 8
(D) \frac{1}{32}
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Step-by-Step Solution

Given |A| = 2, where A is a 2x2 matrix.

We need to find |4A^{-1}|.

Using the property |kA| = k^n |A|, where A is an n x n matrix, we have:

|4A^{-1}| = 4^2 |A^{-1}|

|4A^{-1}| = 16 |A^{-1}|

Also, we know that |A^{-1}| = \frac{1}{|A|}.

So, |A^{-1}| = \frac{1}{2}

Substituting this value, we get:

|4A^{-1}| = 16 * \frac{1}{2}

|4A^{-1}| = 8

Correct Answer: 8

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the properties of determinants and inverse of a matrix to find the value of |4A^{-1}|.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure involving determinant and inverse properties to arrive at the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of standard formulas and properties related to determinants and matrices as covered in the textbook.

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