Class CBSE Class 12 Mathematics Matrices and Determinants Q #748
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
Let A be a square matrix of order 3. If \(|A|=5\), then \(|\operatorname{adj} A|\) is:
(A) 5
(B) 125
(C) 25
(D) -5
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AI Tutor Explanation

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Step-by-Step Solution

We are given that A is a square matrix of order 3 and |A| = 5.

We need to find |adj A|.

We know that for a square matrix A of order n, |adj A| = |A|^(n-1).

In this case, n = 3, so |adj A| = |A|^(3-1) = |A|^2.

Since |A| = 5, we have |adj A| = 5^2 = 25.

Correct Answer: 25

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply the formula relating the determinant of a matrix to the determinant of its adjoint.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to apply a specific procedure or algorithm, which is the formula |adj A| = |A|^(n-1), where n is the order of the matrix.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of a specific formula related to matrices and determinants, which is typically covered in the textbook.

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