If $A$ is an invertible matrix of order $2$ then find $| A^{- 1} |$ .

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Solution

Since $A$ is invertible $\Rightarrow A A^{- 1} = I$
$∴ | A A^{- 1} | = | I |$
$| A | | A^{- 1} | = 1$
$∴ | A^{- 1} | = \frac{1}{| A |}$ .

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