Question

If the adjoint of a $3\times 3$ matrix P is $\left[\begin{array}{ccc}1& 4& 4\\ 2& 1& 7\\ 1& 1& 3\end{array}\right]$, then the possible value(s) of the determinant of P is (are)

• A. $-1$
• B. $-2$
• C. $2$
• D. $1$

Answer 1

Answer: (B), (C)

$2$

$\text{adj P =}\left[\begin{array}{ccc}1& 4& 4\\ 2& 1& 7\\ 1& 1& 3\end{array}\right]$

$|\text{adj P}|=1(3–7)–4(6–7)+4(2–1)=–4+4+4=4$

$\because |\text{adj P}|=|P{|}^2$

$\Rightarrow |P{|}^2=4$

$\Rightarrow |P|=\pm 2$