MathsCBSE Class 12 · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2023-24: question 2

From the official CBSE sample question paper for 2023-24, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQMatrices

If $A$ and $B$ are invertible square matrices of the same order, then which of the following is not correct?

(A) $∣ A B^{- 1} ∣ = \frac{∣ A ∣}{∣ B ∣}$
(B) $∣ (A B)^{- 1} ∣ = \frac{1}{∣ A ∣∣ B ∣}$
(C) $(A B)^{- 1} = B^{- 1} A^{- 1}$
(D) $(A + B)^{- 1} = B^{- 1} + A^{- 1}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Recall the properties of determinants and inverses of products.

Hint 2

Test each statement with $A = B = I$ .

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), (B) and (C) follow from $∣ A B ∣ = ∣ A ∣∣ B ∣$ , $∣ B^{- 1} ∣ = \frac{1}{∣ B ∣}$ and the reversal law $(A B)^{- 1} = B^{- 1} A^{- 1}$ , so they are true.
There is no such rule for the inverse of a sum. For example, with $A = B = I$ : $(2 I)^{- 1} = \frac{1}{2} I$ , whereas $I + I = 2 I$ . So (D) is not correct.
1 mark

Answer: Option (D)

Where the marks are

Identifies $(A + B)^{- 1} = B^{- 1} + A^{- 1}$ as false (1 mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Matrices, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Mathematics sample paper 2023-24: question 2

Hints

Step-by-step solution

Revise the chapter

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