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
Prev Next

AI Tutor Explanation

Powered by Gemini

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

AI generated content. Review strictly for academic accuracy.

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.

More from this Chapter

MCQ_SINGLE
If for a square matrix A, A² - A + I = O then A⁻¹ equals
SUBJECTIVE
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form $AX = B$. (ii) Find $|A|$ and confirm if it is possible to find $A^{-1}$. (iii) (a) Find $A^{-1}$, if possible, and write the formula to find $X$. OR (iii) (b) Find $A^2 - 8I$, where $I$ is an identity matrix.
MCQ_SINGLE
If A and B are square matrices of order m such that \(A^{2}-B^{2}=(A-B)(A+B),\) then which of the following is always correct?
MCQ_SINGLE
If a matrix has 36 elements, the number of possible orders it can have, is:
MCQ_SINGLE
5. The value $|\begin{matrix}x+y & y+z & z+x\\ z & x & y\\ 1 & 1 & 1\end{matrix}|$ is :
View All Questions