Question

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

• A. $$\left[\begin{array}{cc}72& -84\\ -63& 51\end{array}\right]$$
• B. $$\left[\begin{array}{cc}51& 63\\ 84& 72\end{array}\right]$$
• C. $$\left[\begin{array}{cc}51& 84\\ 63& 72\end{array}\right]$$
• D. $$\left[\begin{array}{cc}72& -63\\ -84& 51\end{array}\right]$$

Answer 1

The correct option is B $$\left[\begin{array}{cc}51& 63\\ 84& 72\end{array}\right]$$

$A^2=\left[\begin{array}{cc}16& -9\\ -12& 13\end{array}\right](3A^2+12A)=\left[\begin{array}{cc}72& -63\\ -84& 51\end{array}\right]$
adj$(3A^2+12A)=\left[\begin{array}{cc}51& 63\\ 84& 72\end{array}\right]$