Question

Construct a $2\times 2$ matrix $A=\left[a_{ij}\right]$ whose elements are given by $a_{ij}=ij$

Answer 1

$A=\left[a_{ij}\right]$

$\Rightarrow A={\left[\begin{array}{cc}{a}_{i_1{j}_1}& a_{i_1{j}_2}\\ a_{i_2{j}_1}& a_{i_2{j}_2}\end{array}\right]}_{2\times 2}$

$\Rightarrow a_{ij}=ij$

$\Rightarrow i=1,j=1i.j=1$

$\Rightarrow i=1,j=2i.j=2$

$\Rightarrow i=2,j=1i.j=2$

$\Rightarrow i=2,j=2i.j=4$

$\therefore A=\left[\begin{array}{cc}1& 2\\ 2& 4\end{array}\right]$

Hence, solved.