Class CBSE Class 12 Mathematics Matrices and Determinants Q #762
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2025 MCQ SINGLE
Which of the following can be both a symmetric and skew-symmetric matrix ?
(A) Unit Matrix
(B) Diagonal Matrix
(C) Null Matrix
(D) Row Matrix
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Correct Answer: C

AI Tutor Explanation

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Step-by-Step Solution

  1. A symmetric matrix is a square matrix that is equal to its transpose (A = AT).

  2. A skew-symmetric matrix is a square matrix whose transpose is equal to its negative (AT = -A).

  3. Let's consider a matrix that is both symmetric and skew-symmetric. If A is both, then A = AT and AT = -A. Therefore, A = -A.

  4. This implies that all elements of A must be zero (aij = -aij, which means aij = 0 for all i and j).

  5. Therefore, the matrix must be a null matrix.

Correct Answer: Null Matrix

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to recall the definitions of symmetric and skew-symmetric matrices and apply that understanding to identify which matrix type can satisfy both conditions.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concepts of symmetric and skew-symmetric matrices, and how these properties relate to different types of matrices.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding of matrix types and their properties as covered in the textbook.

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