Question

Let $A=[a_{ij}{]}_{2\times 2},$ where $a_{ij}=(i^2-j^2),$ then, which of the following is correct

• A. $A=\left[\begin{array}{cc}0& -3\\ 3& 0\end{array}\right]$
• B. Trace of $A$ is a negative number
• C. Trace of $A$ is a positive number
• D. $A=\left[\begin{array}{cc}0& -1\\ 3& -3\end{array}\right]$

Answer 1

The correct option is A $A=\left[\begin{array}{cc}0& -3\\ 3& 0\end{array}\right]$

For $A=[a_{ij}{]}_{2\times 2};$ $i=1,2$ and $j=1,2$
Elements of the matrix $A$ are given by
$a_{11}=1^2-1^2=0a_{12}=1^2-2^2=-3a_{21}=2^2-1^2=3a_{22}=2^2-2^2=0$
$\Rightarrow A=\left[\begin{array}{cc}0& -3\\ 3& 0\end{array}\right]$
$\Rightarrow Tr\left(A\right)=0$