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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\textsuperscript{-1}$ \vert $ = 1\\ \\ \vspace{\baselineskip}$ \therefore $ $ \vert $ A\textsuperscript{-1}$ \vert $ = 1/$ \vert $ A$ \vert $ = $ \vert $ A$ \vert $ \textsuperscript{-1}\\ \vspace{\baselineskip}

Thus the statement is false.

Posted by

infoexpert22

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