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Best answer
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$A^{-1} = \frac{adj(A)}{|A|}$

$|A| \cdot A^{-1} = adj(A)$

Multiplying by $A$ (from right) on both sides, we get

$|A| \cdot I = adj(A) \cdot A$

Taking determinant, we get

$|A|^n = |adj(A)| \cdot |A|$

$|adj(A)| = |A|^{n-1}$

So, option (a) is INcorrect.

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I feel it is option b it is the definition of rank

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