Question

A $2\times 2$ matrix whose elements $a_{ij}$ are given by $a_{ij}=i-j$ is

• A. $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$
• B. $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$
• C. $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$

Given, $a_{ij}=i-j$

$a_{11}=1-1=0$

$a_{12}=1-2=-1$

$a_{21}=2-1=1$

$a_{22}=2-2=0$

$\therefore$ Required matrix $=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$