Class CBSE Class 12 Mathematics Matrices and Determinants Q #749
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
If A and B are two square matrices each of order 3 with \(|A|=3\) and \(|B|=5\), then \(|2AB|\) is:
(A) 30
(B) 120
(C) 15
(D) 225
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Step-by-Step Solution

We are given that A and B are square matrices of order 3, with |A| = 3 and |B| = 5.

We need to find |2AB|.

Using the properties of determinants, we know that:

  1. |kA| = kn|A|, where k is a scalar and n is the order of the matrix A.
  2. |AB| = |A||B|

Therefore, |2AB| = 23|AB| = 8|A||B|.

Substituting the given values, we get:

|2AB| = 8 * 3 * 5 = 8 * 15 = 120.

Correct Answer: 120

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply the properties of determinants to calculate the determinant of a matrix expression.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to apply a procedure (using determinant 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 determinant properties as covered in the textbook.

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