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If A is invertible, then A × A⁻¹ equals
AZero matrix (typical)
BIdentity matrix
CA (typical) (typical)
DA⁻¹ (typical)
Answer & Solution
Correct answer: B. Identity matrix
1. By definition, the inverse satisfies A × A⁻¹ = A⁻¹ × A = I (identity matrix).
2. Inverse exists only when |A| ≠ 0.
3. I has 1s on diagonal and 0s elsewhere.
4. Hence (B) is correct.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 1 "Matrices", §1.2 ¶§1.2_
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