First slide

Applications of determinant

Question

If A is a square matrix of order 3 such that |A| = 2, then $|{(adj A^{- 1})}^{- 1}|$ is ___________.

Moderate

Solution

$|adj A^{- 1}| = {|A^{- 1}|}^{2} = \frac{1}{| A |^{2}}$
$\begin{matrix} \Rightarrow |{(adj A^{- 1})}^{- 1}| = \frac{1}{|adj A^{- 1}|} \\ = | A |^{2} = 2^{2} = 4 \end{matrix}$

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