Question

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

• A. $4$
• B. $11$
• C. $5$
• D. $10$

Answer 1

The correct option is B $11$

Given , $adjA=P$
$\Rightarrow |adjA|=|P|$
$\Rightarrow |A{|}^2=2\alpha -6$
$\Rightarrow 16=2\alpha -6$
$\Rightarrow \alpha =11$