If $$P = \left[ {\matrix{
1 & \alpha & 3 \cr
1 & 3 & 3 \cr
2 & 4 & 4 \cr
} } \right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and
$$\left| A \right| = 4,$$ then $$\alpha $$ is equal to :
$$ \Rightarrow {\left| A \right|^2} = \left| P \right|$$
$$ \Rightarrow \left| P \right| = 16$$
$$ \Rightarrow 2\alpha - 6 = 16$$
$$ \Rightarrow \alpha = 11$$
2
AIEEE 2012
MCQ (Single Correct Answer)
Let $$P$$ and $$Q$$ be $$3 \times 3$$ matrices $$P \ne Q.$$ If $${P^3} = {Q^3}$$ and
$${P^2}Q = {Q^2}P$$ then determinant of $$\left( {{P^2} + {Q^2}} \right)$$ is equal to :