If $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$ then $adj\, (3A^2+12A)$ is equal to
Answer & explanation
Correct answer: option 2
We have, $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$
$∴A^2 = AA =\begin{bmatrix}2&-3\\-4&1\end{bmatrix}\begin{bmatrix}2&-3\\-4&1\end{bmatrix}=\begin{bmatrix}19&-9\\-12&13\end{bmatrix}$
$∴3A^2 + 12A =\begin{bmatrix}48&-27\\-36&39\end{bmatrix}+\begin{bmatrix}24&-36\\-48&12\end{bmatrix}=\begin{bmatrix}72&-63\\-84&51\end{bmatrix}$
$⇒adj\,(3A^2 + 12A)=\begin{bmatrix}51&63\\84&72\end{bmatrix}$