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Question

$$A$$ is a $$3 \times 3$$ matrix and $$B$$ is its adjoint matrix. If the determinant of $$B$$ is $$64$$, then the det $$A$$ is 


A
4
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B
±4
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C
±8
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D
8
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Solution

The correct option is C $$\pm 8$$
Given , $$B=adj A$$
$$\Rightarrow |B|=|adj A|$$     ...(1)
We have $$|adj A|=|A|^{n-1}$$ where $$n$$ is the order of matrix A.
Since, $$A$$ is a square matrix of order 3
Then $$|adj A|=|A|^2$$         .....(2)
From (1) and (2), we get
$$64=|A|^2$$
$$\Rightarrow |A|=\pm 8$$

Mathematics

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