Which one of the following statements is true | vedclass

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(C) For option $A$: $A$ non-singular square matrix always has a unique inverse,so this statement is false.For option $B$: By definition,a non-singular

Vedclass · Accepted Answer

If $A' = A$,then $A$ is a square matrix.

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(C) For option $A$: $A$ non-singular square matrix always has a unique inverse,so this statement is false.For option $B$: By definition,a non-singular matrix has a non-zero determinant $(|A| 
eq 0)$,so this statement is false.For option $C$: If $A' = A$,then the number of rows must equal the number of columns,which implies $A$ is a square matrix. Thus,this statement is true.For option $D$: We know that $A \cdot 	ext{adj } A = |A| I_n$. Taking the determinant on both sides,$|A \cdot 	ext{adj } A| = ||A| I_n| = |A|^n |I_n| = |A|^n$. The given expression $|A|^{n-1}$ is incorrect. Therefore,this statement is false.

Which one of the following statements is true?

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