(C) We know that for a square matrix $A$ of order $n$, the determinant of its adjoint matrix is given by $|\operatorname{adj} A| = |A|^{n-1}$.Given th

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(C) We know that for a square matrix $A$ of order $n$, the determinant of its adjoint matrix is given by $|\operatorname{adj} A| = |A|^{n-1}$.Given that $A$ is a $3 \times 3$ matrix, so $n = 3$.Therefore, $|\operatorname{adj} A| = |A|^{3-1} = |A|^2$.Given $|B| = |\operatorname{adj} A| = 64$.So, $|A|^2 = 64$.Taking the square root on both sides, we get $|A| = \pm \sqrt{64} = \pm 8$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Adjoint and inverse of matrices

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Let $A$ be a $3 \times 3$ matrix and $B$ be its adjoint matrix. If $|B|=64,$ then $|A|$ is equal to

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A
$\pm 2$
B
$\pm 4$
C
$\pm 8$
D
$\pm 12$

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Let $A$ be a $3 \times 3$ matrix and $B$ be its adjoint matrix. If $|B|=64,$ then $|A|$ is equal to

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