If $A=\left[\begin{array}{cc}2 & 3 \ -4 & 1\end{array} ight]$, then adj $\left(3 A^2+12 A ight)$ is equal to

Question

If $A=\left[\begin{array}{cc}2 & 3 \ -4 & 1\end{array}ight]$, then adj $\left(3 A^2+12 Aight)$ is equal to

Aicharya · Accepted Answer

$\begin{aligned} & 3 A^2+12 A=3\left[\begin{array}{cc}2 & 3 \ -4 & 1\end{array}ight]^2+12 \ & =3\left[\begin{array}{cc}-8 & 9 \ -12 & -11\end{array}ight]+12\left[\begin{array}{cc}2 & 3 \ -4 & 1\end{array}ight] \ & =\left[\begin{array}{cc}-24+24 & 27+36 \ -36-48 & -33+12\end{array}ight] \ & =\left[\begin{array}{cc}0 & 63 \ -84 & -21\end{array}ight] \ & \Rightarrow \operatorname{adj}\left(3 A^2+12 Aight)=\left[\begin{array}{cc}-21 & -63 \ 84 & 0\end{array}ight]\end{aligned}$

If $A=\left[\begin{array}{cc}2 & 3 \\ -4 & 1\end{array}\right]$, then adj $\left(3 A^2+12 A\right)$ is equal…

Solution