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. $\pm 4$
• C. $\pm 8$
• D. $8$

Answer 1

The correct option is C $\pm 8$

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