CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Q21 Marksmatrix_multiplication

CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Question 2 (Matrices)

For same-order square matrices A and B, which statements always hold? (i) (A+B)(A−B)=A²−B². (ii) AB=BA. (iii) (A+B)²=A²+AB+BA+B². (iv) AB=0 implies A=0 or B=0.

(A) Only (i) and (iii)
(B) Only (ii) and (iii)
(C) Only (iii)
(D) Only (iii) and (iv)

✅ Step-by-Step Solution

Final Answer: Only (iii)

Distributivity proves (iii). Matrix products need not commute, which defeats (i) and (ii). Distinct nonzero diagonal projections onto the two coordinate axes have zero product, defeating (iv).

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CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Question 2 (Matrices)

✅ Step-by-Step Solution

Master Chapter 3: Matrices

All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/2/1

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