Question

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

• A. 4
• B. 11
• C. 5

Answer 1

The correct option is B 11

Given, $P=\left|\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right|$
$\because |P|=1(12-12)-\alpha (4-6)+3(4-6)=2\alpha -6$
$\because$ P=adj (A) [given]
$\therefore |P|=|adjA|=|A{|}^2=16$ $[\because |adjA|=|A{|}^{n-1}]$
$\therefore 2\alpha -6=16$
$\Rightarrow 2\alpha =22$
$\Rightarrow \alpha =11$