Suppose that:
A = $\left[\begin{array}{cc} -3 &2\cr -1 &1 \end{array}\right]$ and B = $\left[\begin{array}{ccc} -1 &2 &3\cr 1 &-3 &-3\cr 4 &4 &4 \end{array}\right]$
Given the following descriptions, determine the following elementary matrices and their inverses.

a. The elementary matrix $E_1$ multiplies the first row of A by $1/3$.
$E_1 =$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$, $E_1^{-1} =$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$
b. The elementary matrix $E_2$ multiplies the second row of A by $-4$.
$E_2 =$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$, $E_2^{-1} =$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$
c. The elementary matrix $E_3$ switches the first and second rows of A.
$E_3 =$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$, $E_3^{-1} =$$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$
d. The elementary matrix $E_4$ adds $3$ times the first row of A to the second row of A.
$E_4 =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$, $E_4^{-1} =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$
e. The elementary matrix $E_5$ multiplies the second row of B by $1/5$.
$E_5 =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$,
$E_5^{-1} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$
f. The elementary matrix $E_6$ multiplies the third row of B by $-2$.
$E_6 =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$,
$E_6^{-1} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$
g. The elementary matrix $E_7$ switches the first and third rows of B.
$E_7 =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$,
$E_7^{-1} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$
h. The elementary matrix $E_8$ adds $5$ times the third row of B to the second row of B.
$E_8 =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$,
$E_8^{-1} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$