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Skew Symmetric Matrix

If A is a ...

Question

If $A$ is a $n \times n$ non singular matrix
Match List 1 with List 2, where $k$ is a scalar

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Solution

By theory of matrices and determinants, we get
$| a d j A | = | A |^{n - 1}$ where A is $n \times n$ matrix.
$(A B)^{- 1} = B^{- 1} A^{- 1}$
$(k A)^{n}$
Take k common from every row.
Now there will n rows.
Hence $k^{n} . A^{n}$
And $A^{- 1} = \frac{a d j A}{| A |}$
Therefore
$a d j A = | A | A^{- 1}$

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