Class CBSE Class 12 Mathematics Matrices and Determinants Q #847
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
A and B are skew-symmetric matrices of same order. AB is symmetric, if:
(A) $AB=O$
(B) $AB=-BA$
(C) $AB=BA$
(D) $BA=O$
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AI Tutor Explanation

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Step-by-Step Solution

Let A and B be skew-symmetric matrices. This means:

AT = -A

BT = -B

Given that AB is symmetric, this means:

(AB)T = AB

Using the property (AB)T = BTAT, we have:

BTAT = AB

Substituting AT = -A and BT = -B, we get:

(-B)(-A) = AB

BA = AB

Correct Answer: AB=BA

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply their knowledge of skew-symmetric and symmetric matrices to determine the condition under which AB is symmetric.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concepts of symmetric and skew-symmetric matrices and their properties, rather than recalling facts or performing routine calculations.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly relates to the properties of matrices, a core topic in the syllabus, and requires recall and application of these properties.

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