If $A =\begin{bmatrix}0&0&\sqrt{3}\\0&\sqrt{3}&0\\\sqrt{3}&0&0\end{bmatrix}$ then $|adj\, A|$ is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 27
$A=\begin{pmatrix} 0&0&\sqrt3\\ 0&\sqrt3&0\\ \sqrt3&0&0 \end{pmatrix}$
Compute determinant of $A$
$|A|=-\sqrt3\begin{vmatrix}0&\sqrt3\\ \sqrt3&0\end{vmatrix}$
$=-\sqrt3(0-3)$
$=3\sqrt3$
For a $3\times3$ matrix
$|\text{adj}\,A|=|A|^{2}$
$=(3\sqrt3)^2$
$=27$
The value of $|\text{adj}\,A|$ is $27$.