Which one of the following statements about a square system is correct?

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

Problem

Which one of the following statements about a square system AX=BAX=B is correct? (a) If ∣A∣≠0|A|\neq 0, the matrix AA is singular. (b) If ∣A∣=0|A|=0 and (adj⁡A)B=0(\operatorname{adj}A)B=0, the system has no solution. (c) If ∣A∣≠0|A|\neq 0, the system has exactly one solution. (d) If ∣A∣=0|A|=0 and (adj⁡A)B≠0(\operatorname{adj}A)B\neq 0, the system has infinitely many solutions.

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