Question

If $A=\left[\begin{array}{cc}2x& 0\\ x& x\end{array}\right]$ and $A^{-1}=\left[\begin{array}{cc}1& 0\\ -1& 2\end{array}\right]$ then the value of $x$ is

• A. 1
• B. 2
• C. $\frac{1}{2}$
• D. None

Answer 1

The correct option is C $\frac{1}{2}$

$A{A}^{-1}=1$
$\therefore \left[\begin{array}{cc}2x& 0\\ x& x\end{array}\right]\left[\begin{array}{cc}1& 0\\ -1& 2\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}2x& 0\\ 0& 2x\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
$\Rightarrow 2x=1$
$\therefore x=\frac{1}{2}$