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  • State True or False for the statements |A-1| ≠ |A|-1, where A is non-singular matrix.

State True or False for the statements

|A^{-1}| \neq |A|^{-1}, where A is non-singular matrix.

Answers (1)

We know A is a non-singular Matrix


In that case: AA\textsuperscript{-1} = I.\\ \\


\\ \vspace{\baselineskip} \Rightarrow \vert A \vert \vert A^{-1} \vert = 1\\ \\ \vspace{\baselineskip} \therefore \vert A^{-1} \vert = 1/ \vert A \vert = \vert A \vert^{-1}\\ \vspace{\baselineskip}

Thus the statement is false.

Posted by

infoexpert22

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