Question

If $A$ is a $3\times 3$ matrix and $B$ is its adjoint such that $\left|B\right|=64$, then $\left|A\right|=$

• A. $64$
• B. $\pm 64$
• C. $\pm 8$
• D. $18$

Answer 1

Answer: (C)

$\pm 8$

Since, A is a order 3 matrix and $B=adjA$
$\Rightarrow$ B is also a order 3 matrix.
Now, since $B=adjA$
$\Rightarrow |B|=|adjA|$
$\Rightarrow 64=|A{|}^2(\because |adjA|=|A{|}^{n-1})$
$\Rightarrow |A|=\pm 8$