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Scalar Matrix

For a 3rd o...

Question

For a $3^{r d}$ order determinant $D$ , its adjoint determinant is

D^{2}

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D

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D^{3}

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D^{4}

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Solution

The correct option is A $D^{2}$
If $A$ is a square matrix of order $n$ .
then, $| a d j (A) | = | A |^{n - 1}$
Given, $| A | = D$ and $n = 3$
Then, $| a d j (A) | = D^{3 - 1} = D^{2}$

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