JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q64

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If $A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}$ , then adj $(3A^2+12A)$ is equal to :

\begin{bmatrix}51&63\\84&72\end{bmatrix}

\begin{bmatrix}51&84\\63&72\end{bmatrix}

\begin{bmatrix}72&-63\\-84&51\end{bmatrix}

\begin{bmatrix}72&-84\\-63&51\end{bmatrix}

Answer and worked solution

Official answer: A

$A^2=\begin{bmatrix}16&-9\\-12&13\end{bmatrix}$ , so $3A^2+12A=\begin{bmatrix}72&-63\\-84&51\end{bmatrix}$ . For a 2×2 matrix the adjoint swaps the diagonal and negates the off-diagonal:
$\text{adj}=\begin{bmatrix}51&63\\84&72\end{bmatrix}.$

Topics:Adjoint and inverse Matrix algebra

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 64