Question

If $P=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]$ is the adjoint of a $3\times 3$ matrix $A$ and $|A|=4$, then $\alpha$ is equal to:

• A. $11$
• B. $5$
• C. $0$
• D. $4$

Answer 1

The correct option is A $11$

$P=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]$
For 3X3 matrix,
$|AdjA|=|A{|}^2$
$|AdjA|=16$
$1(12-12)-\alpha (4-6)+3(4-6)=16$.
$2\alpha -6=16.$
$2\alpha =22.$
$\alpha =11.$