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If A is a 2 × 2 matrix with det(A) = d, then A^{-1} exists provided
Ad = 0
Bd > 0 only
CA is symmetric only
Dd ≠ 0
Answer & Solution
Correct answer: D. d ≠ 0
1. The inverse formula A^{-1} = (1/det A) adj(A) divides by det(A).
2. Division is valid only when det(A) ≠ 0.
3. Hence A is invertible iff d ≠ 0.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 2 "Matrices" §2.6_
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