Question

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

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

Answer 1

Answer: (A)

$\left[\begin{array}{cc}51& 63\\ 84& 72\end{array}\right]$

$\begin{array}{c}A=\left[\begin{array}{cc}2& -3\\ -4& 1\end{array}\right]\\ A^2=\left[\begin{array}{cc}2& -3\\ -4& 1\end{array}\right]\left[\begin{array}{cc}2& -3\\ -4& 1\end{array}\right]\\ =\left[\begin{array}{cc}16& -9\\ -12& 13\end{array}\right]\\ Now,\\ \left(3A^2+12A\right)=\left[\begin{array}{cc}48& -27\\ -36& 39\end{array}\right]+\left[\begin{array}{cc}24& -36\\ -48& 12\end{array}\right]\\ =\left[\begin{array}{cc}72& -63\\ -84& 51\end{array}\right]\\ adj.\left(3A^2+12A\right)=\left[\begin{array}{cc}51& 63\\ 84& 72\end{array}\right]\\ Hence,theoptionAiscorrectanswer.\end{array}$