If A=[aij] is a square matrix of order 2 such that aij=cases1, & when i≠ j\\ 0, & when i=jcases, then A² is (A) bmatrix1&0\\1&0bmatrix2×2 (B) bmatrix1&1\\0&0bmatrix2×2 (C) bmatrix1&1\\1&0bmatrix2×2 (D) bmatrix1&0\\0&1bmatrix2×2

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

CBSE Class 12 Mathematics sample paper 2023-24: question 1

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

Q1 · 1 mark · MCQMatrices

If $A = [a_{ij}]$ is a square matrix of order 2 such that $a_{ij} = {1, 0, when i \neq = j when i = j$ , then $A^{2}$ is

(A) $[1100]_{2 \times 2}$
(B) $[1010]_{2 \times 2}$
(C) $[1110]_{2 \times 2}$
(D) $[1001]_{2 \times 2}$

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

Write down each entry of $A$ using the rule given.

Hint 2

Multiply $A$ by itself, row into column.

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.

Here $a_{11} = a_{22} = 0$ and $a_{12} = a_{21} = 1$ , so $A = [0110]$ .
$A^{2} = [0 \cdot 0 + 1 \cdot 1 1 \cdot 0 + 0 \cdot 1 0 \cdot 1 + 1 \cdot 0 1 \cdot 1 + 0 \cdot 0] = [1001]$ , which is option (D).
1 mark

Answer: $A^{2} = I$ , option (D)

Where the marks are

Writes $A$ correctly and squares it to get $I$ (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 1

Hints

Step-by-step solution

Revise the chapter

More questions from Matrices