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  • Fill in the blanks If A is invertible matrix of order 3 × 3, then |A-1|= ____.

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If A is invertible matrix of order 3 × 3, then |A^{-1}|= ____.

Answers (1)

If A is invertible matrix of order 3 $ \times $ 3, then $ \vert $ A\textsuperscript{-1}$ \vert $ = $ \vert $ A$ \vert $ \textsuperscript{-1}\\

Given 

A = invertible matrix 3x3
\\\vspace{\baselineskip} \uline{ }AA\textsuperscript{-1} = I.\\ \\ \vspace{\baselineskip}$ \Rightarrow $ $ \vert $ A$ \vert $ $ \vert $ A\textsuperscript{-1}$ \vert $ = 1\\ \\

\therefore\left|A^{-1}\right|=\frac{1}{|A|} \\

Posted by

infoexpert22

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