Discussion Forum

1)

If the adjoint of a 3x 3 matrix P is 

$\begin{bmatrix}1 & 4&4 \\2 & 1&7\\1&1&3 \end{bmatrix}$, then the possible value(s) of the determinant of P is,/are

Answer:

Option A,D

Explanation:

 Concept involved  if $|A_{n xn}|=\triangle$,  then   $|adj A|= \triangle ^{n-1}$

So., Here,$adj  P_{3x3}$=$\begin{bmatrix}1 & 4&4 \\2 & 1&7\\1&1&3 \end{bmatrix}$

 $\Rightarrow$    $|adj P|=|P|^{2}$

 $\therefore$   $|adj P|$= $\begin{bmatrix}1 & 4&4 \\2 & 1&7\\1&1&3 \end{bmatrix}$

  =1(3-7)-4(6-7)+4(2-1)

=-4+4+4=4

|P|= $\pm 2$