CBSE 2026 · Region 2 · Set 1 · Q2 · 1 mark
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 $\displaystyle \mathrm{B}=0$
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
From CBSE’s own marking scheme for this paper.
(C)
Only (iii)
MatricesOperations on MatricesAnalysemcqmedium
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 · asked 3×
- Given A=[ ] and B=[ ], find AB. Hence, solve the system of linear equations: OR If A=[ ], then find A^-1.…2025 · asked 3×
- Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB+3(AB+BA)-4 BA, where A and B are both…2025 · asked 3×
- Three students, Neha, Rani and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads…2025 · asked 3×
- If inverse of matrix [ ] is the matrix [ ], then value of λ is:2024 · asked 3×
- If A=[ ] and (3 I+4 A)(3 I-4 A)=x^2 I, then the value (s) x is/are:2023 · asked 3×
- If A=[ ], find A^-1 and use it to solve the following system of equations: -2 y+z=7,2 x-y-z=8, x-2 y=10 OR If…2026 · asked 3×
- What is the total number of possible matrices of order 3 × 3 with each entry as √2 or √3?2025 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.