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
If $\begin{vmatrix}-1&-2&5\\-2&a&-1\\0&4&2a\end{vmatrix}=-86$, then the sum of all possible values of a is
MCQ_SINGLE
If \(\begin{bmatrix}4+x&x-1\\ -2&3\end{bmatrix}\) is a singular matrix, then the value of x is:
MCQ_SINGLE
The value $|\begin{bmatrix}x+y & y+z & z+x\\ z & x & y\\ 1 & 1 & 1\end{bmatrix}|$ is :
MCQ_SINGLE
If $\begin{bmatrix}4\\1\\3\end{bmatrix}A=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$, then order of A must be:
MCQ_SINGLE
If \(\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix},\) then the value of \((x-y)\) is :
View All Questions