Question

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

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

Answer 1

The correct option is C $\pm 8$

$|\text{adj}A|=|A{|}^{n-1}$ where $n$ is the order of the square matirx.
Hence $|B|=|\text{adj}A|=|A{|}^{3-1}$
$=|A{|}^2$
Therefore
$|A|=\sqrt{|B|}=\sqrt{64}=\pm 8$.