Use the Inverse Formula $A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c } d & - b \\- c & a\end{array} \right]$

Multiple Choice

Use the inverse formula $A ^ { - 1 } = \frac { 1 } { a d - b c } \left[ \begin{array} { c c } d & - b \\- c & a\end{array} \right]$ to find the inverse of the 2×2 matrix (if it exists) .
$\left[ \begin{array} { c c } 1 & - 2 \\- 3 & 2\end{array} \right]$

A) $- \frac { 1 } { 4 } \left[ \begin{array} { c c } - 2 & - 2 \\3 & 1\end{array} \right]$
B) $- \frac { 1 } { 4 } \left[ \begin{array} { l l } - 2 & - 2 \\- 3 & - 1\end{array} \right]$
C) $- \frac { 1 } { 4 } \left[ \begin{array} { l l } 2 & 2 \\3 & 1\end{array} \right]$
D) $- \frac { 1 } { 4 } \left[ \begin{array} { c c } - 2 & 2 \\3 & - 1\end{array} \right]$
E) $- \frac { 1 } { 4 } \left[ \begin{array} { c c } 2 & - 2 \\3 & 1\end{array} \right]$