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
B
±4
C
±8
D
8

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 3Then $$|adj A|=|A|^2$$         .....(2)From (1) and (2), we get$$64=|A|^2$$$$\Rightarrow |A|=\pm 8$$Mathematics

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