Which of the following conditions is both necessary and sufficient for a matrix to…

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

Problem

Which of the following conditions is both necessary and sufficient for a 3×33\times 3 matrix AA to possess an inverse? (a) rank⁡(A)=2\operatorname{rank}(A)=2 (b) det⁡(A)≠0\det(A)\neq 0 (c) det⁡(A)>0\det(A)>0 (d) trace⁡(A)≠0\operatorname{trace}(A)\neq 0

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