✓ Board-verified
Mathematics · 2026 · 1 mark
CBSE 2026 · Region 2 · Set 1 · Q2
If A and B are square matrices of same order, then which of the following statements is/are always true? (i) ( A + B )( A - B )= A^2- B^2 (ii) AB =…
If A and B are square matrices of same order, then which of the following statements is/are always true ?
(i)
$\displaystyle (\mathrm{A}+\mathrm{B})(\mathrm{A}-\mathrm{B})=\mathrm{A}^{2}-\mathrm{B}^{2}$
(ii)
$\displaystyle \mathrm{AB}=\mathrm{BA}$
(iii)
$\displaystyle (\mathrm{A}+\mathrm{B})^{2}=\mathrm{A}^{2}+\mathrm{AB}+\mathrm{BA}+\mathrm{B}^{2}$
(iv)
$\displaystyle \mathrm{AB}=0 \Rightarrow \mathrm{~A}=0$ or $\displaystyle \mathrm{B}=0$
Official answer
(C)
Only (iii)
More from Matrices
- Let both AB^′ and B^′ A be defined for matrices A and B. If order of A is n × m, then the order of B is:2025
- Given A= [-4, 4, 4; -7, 1, 3; 5, -3, -1] and B= [1, -1, 1; 1, -2, -2; 2, 1, 3], find AB. Hence, solve the system of linear equations: x-y+z=4; x-2…2025
- If a matrix A is both symmetric and skew-symmetric, then A is a:2025
- If A= [x, 0; 1, 1] and B= [4, 0; -1, 1], then value of x for which A^2=B is:2024
- If A= [1, 2, 3; 3, -2, 1; 4, 2, 1], then show that A^3-23 A-40 I=O.2023
- If [x, 2, 0] [5; -1; x] = [3, 1] [-2; x], then value of x is:2024
- If A= [0, -3, 8; 3, 0, 5; -8, -5, 0], then A is a:2025
- Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB+3(AB+BA)-4 BA, where A and B are both matrices of order 2 × 2. It is known…2025
CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.