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प्रश्न
Let \(B\) and \(C\) be two inverses of a square matrix \(A\). Which chain correctly proves that \(B=C\)?
पर्याय
\[B=BI=B(AC)=(BA)C=IA=A\]
\[B=BI=B(AC)=(BA)C=IC=C\]
\[B=BI=B(AC)=(AB)C=IC=C\]
\[B=BI=B(CA)=(BA)C=IC=C\]
MCQ
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उत्तर
Since \(AC=I\), \(B(AC)=BI=B\). Also, \(BA=I\), so \((BA)C=IC=C\); therefore \(B=C\), proving uniqueness.
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