MathsCBSE Class 12 · Board exam 2026, set 65/1/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2026: question 6

Set in the CBSE Class 12 board exam of 2026, paper 65/1/1, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQMatrices

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 65/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Use $A^{'} = - A$ and $B^{'} = - B$ .

Hint 2

Take the transpose of each option and compare with its negative.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$A^{'} = - A, B^{'} = - B$ . Then $(A - B)^{'} = A^{'} - B^{'} = - A + B = - (A - B)$ , so $A - B$ is skew symmetric.
1 mark
$(A B)^{'} = B^{'} A^{'} = B A$ , $(A B + B A)^{'} = A B + B A$ (symmetric), $((A + B)^{2})^{'} = (A + B)^{2}$ (symmetric); these fail. Option (D).

Answer: $A - B$ , option (D)

Where the marks are

Shows $(A - B)^{'} = - (A - B)$ (1 mark)

Revise the chapter

Chapter: Matrices (notes, formulas, where marks are lost and every past question)
Topic: Symmetric and Skew-Symmetric Matrices

Practise this chapterBoard-style questions from Matrices, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2026: question 6

Hints

Step-by-step solution

Revise the chapter

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