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Question

If a $$n\times n$$ square matrix $$A$$ is such that $$\left| A \right| =D$$ and $$\left| adj\quad A \right| =D'$$, then-


A
DD=Dn
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B
DD=Dn1
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C
DD=D2
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D
none of these
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Solution

The correct option is B $$DD'={D}^{n}$$
Considering that $$A$$ is an nth order square matrix, then
$$|adjA|=|A|^{n-1}$$
Now it is given that
$$|adjA|=D'$$ and $$|A|=D$$.
Hence
$$D'=D^{n-1}$$
Or
$$D'=\dfrac{D^{n}}{D}$$
Or
$$D.D'=D^{n}$$

Applied Mathematics

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