Class CBSE Class 12 Mathematics Matrices and Determinants Q #1843
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric ?
(A) $AB$
(B) $AB + BA$
(C) $(A + B)^2$
(D) $A - B$
Prev Finish
Correct Answer: D

AI Tutor Explanation

Powered by Gemini

Detailed Solution

Step 1: Understand the properties of skew-symmetric matrices

A matrix A is skew-symmetric if AT = -A. Given that A and B are skew-symmetric, we have AT = -A and BT = -B.

Step 2: Evaluate Option (D)

Let C = A - B. To check if C is skew-symmetric, we find its transpose:

$$C^T = (A - B)^T = A^T - B^T$$

Substituting the properties of skew-symmetric matrices:

$$C^T = (-A) - (-B) = -A + B = -(A - B) = -C$$

Since CT = -C, the matrix A - B is skew-symmetric.

Step 3: Verify other options

For (A), (AB)T = BTAT = (-B)(-A) = BA, which is not necessarily -AB. For (B), (AB + BA)T = (AB)T + (BA)T = BTAT + ATBT = BA + AB, which is symmetric. For (C), ((A+B)^2)^T = (A+B)^T(A+B)^T = (-A-B)(-A-B) = (A+B)^2, which is symmetric.

Final Answer: D

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to utilize the definition and properties of transpose and skew-symmetric matrices to verify algebraic expressions.
Knowledge Dimension: CONCEPTUAL
Justification: The student must understand the underlying mathematical concepts of matrix operations and symmetry properties rather than just recalling a formula.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This question tests the student's ability to manipulate matrix algebra under specific constraints, which is a core competency in the Matrices chapter.

More from this Chapter

MCQ_SINGLE
Let A be a $3\times3$ matrix such that | adj A|=64. Then |A| is equal to:
MCQ_SINGLE
If \(A=[a_{ij}]\) is an identity matrix, then which of the following is true ?
LA
Given that $P=\begin{bmatrix}2&-1\\3&4\end{bmatrix}$, $Q=\begin{bmatrix}5&2\\7&4\end{bmatrix}$ and $R=\begin{bmatrix}2&5\\3&8\end{bmatrix}$, find a matrix S such that PQ - RS is a null matrix.
MCQ_SINGLE
If $A=\begin{bmatrix}1&4&x\\ z&2&y\\ -3&-1&3\end{bmatrix}$ is a symmetric matrix, then the value of $x+y+z$ is :
LA
If $A=\begin{bmatrix}1&cot~x\\ -cot~x&1\end{bmatrix}$ show that $A^{\prime}A^{-1}=\begin{bmatrix}-cos~2x&-sin~2x\\ sin~2x&-cos~2x\end{bmatrix}$
View All Questions