Give a $3 \times 3$ elementary matrix $E$ which will carry out the row operation $R_{1} \leftrightarrow R_{3}$.

$E =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$

Test that $E$ actually works for carrying out this row operation by computing the product $E A$ for the matrix $$A = \left[\begin{array}{cccc} -3 &1 &-3 &3\cr 5 &-3 &2 &-1\cr 1 &-1 &2 &3 \end{array}\right].$$
$EA =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$