Question

If two matrices $A=\left[\begin{array}{cc}2x& 2\\ 1& y\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -2\\ 2& 1\end{array}\right]$ are such that $BA=O.$ Then $(x,y)$ is

• A. $(1,1)$
• B. $(-\frac{1}{4},-4)$
• C. $(\frac{1}{4},4)$
• D. No value of $(x,y)$ exists.

Answer 1

The correct option is D No value of $(x,y)$ exists.

$BA=\left[\begin{array}{cc}1& -2\\ 2& 1\end{array}\right]\left[\begin{array}{cc}2x& 2\\ 1& y\end{array}\right]=\left[\begin{array}{cc}2x-2& 2-2y\\ 4x+1& 4+y\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$
Equating element in first row,
$\Rightarrow 2x-2=0$ and $2-2y=0$
$\Rightarrow x=1,y=1$
Equating elements from second row, we get
$4x+1=0$ and $4+y=0$
as $(1,1)$ does not satisfy above equations.
$\therefore$ No possible value of $(x,y)$ exists such that $BA=O.$