Class CBSE Class 12 Mathematics Matrices and Determinants Q #743
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
If A and B are two non-zero square matrices of same order such that \((A+B)^{2}=A^{2}+B^{2}\) then :
(A) \(AB=O\)
(B) \(AB=-BA\)
(C) \(BA=O\)
(D) \(AB=BA\)
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AI Tutor Explanation

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Step-by-Step Solution

Given: \((A+B)^{2}=A^{2}+B^{2}\)

Expanding the left side, we have: \((A+B)^{2} = (A+B)(A+B) = A^{2} + AB + BA + B^{2}\)

So, \(A^{2} + AB + BA + B^{2} = A^{2} + B^{2}\)

Subtracting \(A^{2}\) and \(B^{2}\) from both sides, we get: \(AB + BA = O\)

Therefore, \(AB = -BA\)

Correct Answer: \(AB = -BA\)<\/strong>

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the algebraic identity of \((A+B)^2\) and the properties of matrix multiplication to derive the relationship between A and B.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concepts of matrix addition, matrix multiplication, and algebraic identities in the context of matrices. It's not just about recalling facts but applying the concepts.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of matrix algebra, which is a core topic in the syllabus.

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