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

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

Aicharya · Accepted Answer

We know for a third order matrix $P$, $|\operatorname{Adj} P|=|P|^{2}$ Where $\begin{aligned} &|\operatorname{Adj} P|=1(3-7)-4(6-7)+4(2-1)=4 \ 	herefore \quad &|P|^{2}=4 \mathrm{P}|P|=2 	ext { or }-2 \end{aligned}$

If the adjoint of a $3 \times 3$ matrix $P$ is $\left[\begin{array}{lll}1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 &…

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