Question

Let $A$ be a matrix such that $A\cdot \left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$ is a scalar matrix and $|3A|=108.$ Then $A\cdot \left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$is equal to

• A. $\left[\begin{array}{cc}4& -32\\ 0& 36\end{array}\right]$
• B. $\left[\begin{array}{cc}36& 72\\ 0& 108\end{array}\right]$
• C. $\left[\begin{array}{cc}4& 0\\ -32& 36\end{array}\right]$
• D. $\left[\begin{array}{cc}36& -32\\ 0& 4\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{cc}36& 72\\ 0& 108\end{array}\right]$

$\begin{array}{c}Wehave\\ \left|3A\right|=108\\ A=36\\ Now,\\ A.\left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]\\ =36\left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]\\ =\left[\begin{array}{cc}36& 72\\ 0& 108\end{array}\right]\end{array}$

Hence, option $B$ is the correct answer.