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

(C) $\left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right]$

(A) $\left[\begin{array}{rr}72 & -63 \\ -84 & 51\end{array}\right]$

(B) $\left[\begin{array}{rr}72 & -84 \\ -63 & 51\end{array}\right]$

(D) $\left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right]$

JEE Main · 2017 · 02 Apr 2017 · Offline · Matrices

A = [2 - 4 - 3 1]

, then

adj (3 A^{2} + 12 A)

is equal to :

Answer: (C)

First

A^{2} = [16 - 12 - 9 13]

, so

3 A^{2} = [48 - 36 - 27 39]

and

12 A = [24 - 48 - 36 12]

, giving

3 A^{2} + 12 A = [72 - 84 - 63 51]

. For a

2 \times 2

matrix the adjugate swaps the diagonal entries and flips the sign of the off-diagonal ones, so

adj (3 A^{2} + 12 A) = [51846372]

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option