If then adj (3A^{2} + 12A) is equal to

**Solution**

\( A^2 = \begin{bmatrix}2 & -3 \\-4 & 1 \end{bmatrix}\begin{bmatrix}2 & -3 \\-4 & 1 \end{bmatrix} \)

\( A^2 = \begin{bmatrix}16 & -9 \\-12 & 13 \end{bmatrix} \)

\( 3A^2 + 12A = \begin{bmatrix}72 & -63 \\-84 & 51 \end{bmatrix} \)

\( Adj (3A^2 + 12A) = \begin{bmatrix}51 & 63 \\84 & 72 \end{bmatrix} \)

**The correct option is B.**