Class CBSE Class 12 Mathematics Matrices and Determinants Q #752
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2025 MCQ SINGLE
Sum of two skew-symmetric matrices of same order is always a/an:
(A) skew-symmetric matrix
(B) symmetric matrix
(C) null matrix
(D) identity matrix
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Step-by-Step Solution

  1. Let A and B be two skew-symmetric matrices of the same order. This means that AT = -A and BT = -B.
  2. Let C = A + B. We want to determine if C is skew-symmetric, symmetric, null, or identity.
  3. To check if C is skew-symmetric, we need to find CT. CT = (A + B)T = AT + BT.
  4. Since A and B are skew-symmetric, AT = -A and BT = -B. Therefore, CT = -A - B = -(A + B) = -C.
  5. Since CT = -C, C is a skew-symmetric matrix.

Correct Answer: skew-symmetric matrix

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to comprehend the properties of skew-symmetric matrices and apply that understanding to determine the nature of their sum.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of skew-symmetric matrices and their properties under addition, rather than rote memorization of facts.
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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