For the matrix equation

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

For the matrix equation AX=BAX=B, which of the following conditions ensures that the system has infinitely many solutions? (a) ∣A∣=0 and (adj⁡A)B≠0|A|=0 \text{ and } (\operatorname{adj}A)B\neq 0 (b) ∣A∣≠0 and (adj⁡A)B=0|A|\neq 0 \text{ and } (\operatorname{adj}A)B=0 (c) ∣A∣=0 and (adj⁡A)B=0|A|=0 \text{ and } (\operatorname{adj}A)B=0 (d) ∣A∣≠0 and (adj⁡A)B≠0|A|\neq 0 \text{ and } (\operatorname{adj}A)B\neq 0

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