Given \[{{a}_{i\text{ }j}}~=\text{ }{{e}^{2ix}}~sin\text{ }x\text{ }j\]

Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 2}}\]

So, the elements in a \[2\text{ }\times \text{ }2\] matrix are

\[{{a}_{11}},\text{ }{{a}_{12}},\text{ }{{a}_{21}},\text{ }{{a}_{22}},\]

\[{{a}_{11}}~=\]

\[{{a}_{12}}~=\]

\[{{a}_{21}}~=\]

\[{{a}_{22}}~=\]

Substituting these values in matrix A we get,